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1.
We approach the problem of uniformization of general Riemann surfaces through consideration of the curvature equation, and
in particular the problem of constructing Poincaré metrics (i.e., complete metrics of constant negative curvature) by solving
the equation Δu-e
2u=Ko(z) on general open surfaces. A few other topics are discussed, including boundary behavior of the conformal factore
2u giving the Poincaré metric when the Riemann surface has smoothly bounded compact closure, and also a curvature equation proof
of Koebe's disk theorem.
Research supported in part by NSF Grant DMS-9971975 and also at MSRI by NSF grant DMS-9701755.
Research supported in part by NSF Grant DMS-9877077 相似文献
2.
V. V. Makeev 《Journal of Mathematical Sciences》1998,91(6):3518-3525
Five theorems on polygons and polytopes inscribed in (or circumscribed about) a convex compact set in the plane or space are
proved by topological methods. In particular, it is proved that for every interior point O of a convex compact set in ℝ3, there exists a two-dimensional section through O circumscribed about an affine image of a regular octagon. It is also proved
that every compact convex set in ℝ3 (except the cases listed below) is circumscribed about an affine image of a cube-octahedron (the convex hull of the midpoints
of the edges of a cube). Possible exceptions are provided by the bodies containing a parallelogram P and contained in a cylinder
with directrix P. Bibliography: 29 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 286–298.
Translated by B. M. Bekker. 相似文献
3.
Boris Aronov Bernard Chazelle Herbert Edelsbrunner Leonidas J. Guibas Micha Sharir Rephael Wenger 《Discrete and Computational Geometry》1991,6(1):435-442
We prove that for any setS ofn points in the plane andn
3−α triangles spanned by the points inS there exists a point (not necessarily inS) contained in at leastn
3−3α/(c log5
n) of the triangles. This implies that any set ofn points in three-dimensional space defines at most
halving planes.
Work on this paper by Boris Aronov and Rephael Wenger has been supported by DIMACS under NSF Grant STC-88-09648. Work on this
paper by Bernard Chazelle has been supported by NSF Grant CCR-87-00917. Work by Herbert Edelsbrunner has been supported by
NSF Grant CCR-87-14565. Micha Sharir has been supported by ONR Grant N00014-87-K-0129, by NSF Grant CCR-89-01484, and by grants
from the U.S.-Israeli Binational Science Foundation, the Israeli National Council for Research and Development, and the Fund
for Basic Research administered by the Israeli Academy of Sciences. 相似文献
4.
H. W. Buff 《Algebra Universalis》1985,21(2-3):234-249
In (2) Chang introduced the notion ofMV-algebra in order to show completeness of many-valued Lukasiewicz-logic. Using a characterisation ofMV-algebras in a simpler language, proposed by H. Läuchli, this article shows the undecidability of the elementary theory ofMV-algebras by reducing it to the undecidability of lattice-ordered abelian groups (Gurevich). Further it is shown that the wordproblem forMV-algebras is solvable and that the elementary theories of finite-orderMV-algebras are decidable.I wish to thank Prof. H. Läuchli for his idea to describeMV-aigebras by the truncated difference and for a lot of fruitful talks about the subject.Presented by S. Burris. 相似文献
5.
L. L. Maksimova 《Algebra and Logic》2006,45(1):49-66
We look at the interplay between the projective Beth property in non-classical logics and interpolation. Previously, we proved
that in positive logics as well as in superintuitionistic and modal ones, the projective Beth property PB2 follows from Craig's interpolation property and implies the restricted interpolation property IPR. Here, we show that IPR and PB2 are equivalent in positive logics, and also in extensions of the superintuitionistic logic KC and of the modal logic Grz.2.
Supported by RFBR grant No. 06-01-00358, by INTAS grant No. 04-77-7080, and by the Council for Grants (under RF President)
and State Aid of Fundamental Science Schools, project NSh-2069.2003.1.
__________
Translated from Algebra i Logika, Vol. 45, No. 1, pp. 85–113, January–February, 2006. 相似文献
6.
Steven G. Krantz 《Journal of Functional Analysis》1979,34(3):456-471
It is known that a function on n which can be well approximated by polynomials, in the mean over Euclidean balls, is Lipschitz smooth in the usual sense. In this paper an analogous theorem is proved in which n is replaced by a set X, the averages over balls are replaced by a family of sublinear operators satisfying certain axioms, and the polynomials are replaced by a class of functions having certain regularity properties with respect to the averaging operators. Applications are given to function theory on domains in n, to nilpotent Lie groups, and to the classical Euclidean case. The first application provides a characterization of the duals of Hardy spaces on the ball in n. 相似文献
7.
We study the topology of (properly) immersed complete minimal surfaces P 2 in Hyperbolic and Euclidean spaces which have finite total extrinsic curvature, using some isoperimetric inequalities satisfied by the extrinsic balls in these surfaces (see [10]). We present an alternative and unified proof of the Chern-Osserman inequality satisfied by these minimal surfaces (in ? n and in ? n (b)), based in the isoperimetric analysis mentioned above. Finally, we show a Chern-Osserman-type equality attained by complete minimal surfaces in the Hyperbolic space with finite total extrinsic curvature. 相似文献
8.
The overlay of 2≤m≤d minimization diagrams of n surfaces in ℝ
d
is isomorphic to a substructure of a suitably constructed minimization diagram of mn surfaces in ℝ
d+m−1. This elementary observation leads to a new bound on the complexity of the overlay of minimization diagrams of collections
of d-variate semi-algebraic surfaces, a tight bound on the complexity of the overlay of minimization diagrams of collections of
hyperplanes, and faster algorithms for constructing such overlays. Further algorithmic implications are discussed.
Work by V. Koltun was supported by NSF CAREER award CCF-0641402.
Work by M. Sharir was supported by NSF Grants CCR-00-98246 and CCF-05-14079, by a grant from the Israeli Academy of Sciences
for a Center of Excellence in Geometric Computing at Tel Aviv University, and by the Hermann Minkowski Minerva Center for
Geometry at Tel Aviv University. 相似文献
9.
Pankaj K. Agarwal Rolf Klein Christian Knauer Stefan Langerman Pat Morin Micha Sharir Michael Soss 《Discrete and Computational Geometry》2008,39(1-3):17-37
The detour and spanning ratio of a graph G embedded in
measure how well G approximates Euclidean space and the complete Euclidean graph, respectively. In this paper we describe O(nlog n) time algorithms for computing the detour and spanning ratio of a planar polygonal path. By generalizing these algorithms,
we obtain O(nlog 2
n)-time algorithms for computing the detour or spanning ratio of planar trees and cycles. Finally, we develop subquadratic
algorithms for computing the detour and spanning ratio for paths, cycles, and trees embedded in
, and show that computing the detour in
is at least as hard as Hopcroft’s problem.
This research was partly funded by CRM, FCAR, MITACS, and NSERC. P.A. was supported by NSF under grants CCR-00-86013 EIA-99-72879,
EIA-01-31905, and CCR-02-04118, by ARO grants W911NF-04-1-0278 and DAAD19-03-1-0352, and by a grant from the U.S.-Israeli
Binational Science Foundation. R.K. was supported by DFG grant Kl 655/14-1. M.S. was supported by NSF Grants CCR-97-32101
and CCR-00-98246, by a grant from the U.S.-Israeli Binational Science Foundation (jointly with P.A.), by a grant from the
Israeli Academy of Sciences for a Center of Excellence in Geometric Computing at Tel Aviv University, and by the Hermann Minkowski–MINERVA
Center for Geometry at Tel Aviv University.
Some of these results have appeared in a preliminary form in [2, 20]. 相似文献
10.
V. Elser 《Discrete and Computational Geometry》2001,25(3):445-476
The level set of an elliptic function is a doubly periodic point set in ℂ. To obtain a wider spectrum of point sets, we consider,
more generally, a Riemann surface S immersed in ℂ2 and its sections (“cuts”) by ℂ More specifically, we consider surfaces S defined in terms of a fundamental surface element obtained as a conformai map of triangular domains in ℂ. The discrete group
of isometries of ℂ2 generated by reflections in the triangle edges leaves S invariant and generalizes double-periodicity. Our main result concerns the special case of maps of right triangles, with
the right angle being a regular point of the map. For this class of maps we show that only seven Riemann surfaces, when cut,
form point sets that are discrete in ℂ. Their isometry groups all have a rank 4 lattice subgroup, but only three of the corresponding
point sets are doubly periodic in ℂ. The remaining surfaces form quasiperiodic point sets closely related to the vertex sets
of quasiperiodic tilings. In fact, vertex sets of familiar tilings are recovered in all cases by applying the construction
to a piecewise flat approximation of the corresponding Riemann surface. The geometry of point sets formed by cuts of Riemann
surfaces is no less “rigid” than the geometry determined by a tiling, and has the distinct advantage in having a regular behavior
with respect to the complex parameter which specifies the cut. 相似文献
11.
Hilja L. Huru 《Acta Appl Math》2008,101(1-3):121-132
We present a method for quantizing semisimple Lie algebras. In Huru (Russ. Math. [2007]) we defined quantizations of the braided Lie algebra structure on a finite dimensional graded vector space V by quantizations of braided derivations on the exterior algebra of V
*
. We find quantizations of semisimple Lie algebras in this setting using the grading by their roots and shall go through all
root systems, classical and exceptional.
相似文献
12.
This paper provides some useful results for convex risk measures. In fact, we consider convex functions on a locally convex vector space E which are monotone with respect to the preference relation implied by some convex cone and invariant with respect to some numeraire (‘cash’). As a main result, for any function f, we find the greatest closed convex monotone and cash-invariant function majorized by f. We then apply our results to some well-known risk measures and problems arising in connection with insurance regulation. 相似文献
13.
The concepts of k-systems, k-networks and k-covers were defined by A. Arhangel’skii in 1964, P. O’Meara in 1971 and R. McCoy, I. Ntantu in 1985, respectively. In this
paper the relationships among k-systems, k-networks and k-covers are further discussed and are established by mk-systems. As applications, some new characterizations of quotients or closed images of locally compact metric spaces are given
by means of mk-systems. 相似文献
14.
M. I. Golenishcheva-Kutuzova D. R. Lebedev 《Functional Analysis and Its Applications》1999,33(4):241-259
The fermionic approach to the Kadomtsev-Petviashvili hierarchy, suggested by the Kyoto school (Sato, Date, Jimbo, Kashiwara,
and Miwa) in 1981–4, is generalized on the basis of the idea that, in a sense, the components of intertwining operators are
a generalization of free fermions forgl
∞. Integrable hierarchies related to symmetries of Kac-Moody algebras are described in terms of intertwining operators. The
bosonization of these operators for various choices of the Heisenberg subalgebra is explicity written out. These various realizations
result in distinct hierarchies of soliton equations. For example, forsl
N
-symmetries this gives the hierarchies obtained by the (n
1,...,n
s
)-reduction from thes-component KP hierarchy introduced by Kac and van de Leur.
The research of both authors was supported in part by RFBR grant No. 96-02-18046, grant No. 96-15-96455 for the support of
leading scientific schools, and RFBR-CNRS grant No. 98-01-22033.
International Center for Nonlinear Science at the Landau Institute of Theoretical Physics. Institute of Theoretical and Experimental
Physics. Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 33, No. 4, pp. 1–24, October–December, 1999.
Translated by M. I. Golenishcheva-Kutuzova 相似文献
15.
Daniel Gon?alves Benjamin Lévêque Alexandre Pinlou 《Discrete and Computational Geometry》2012,48(1):239-254
A?contact representation by triangles of a graph is a set of triangles in the plane such that two triangles intersect on at most one point, each triangle represents a vertex of the graph and two triangles intersects if and only if their corresponding vertices are adjacent. De Fraysseix, Ossona de Mendez and Rosenstiehl proved that every planar graph admits a contact representation by triangles. We strengthen this in terms of a simultaneous contact representation by triangles of a planar map and of its dual. A?primal?Cdual contact representation by triangles of a planar map is a contact representation by triangles of the primal and a contact representation by triangles of the dual such that for every edge uv, bordering faces f and g, the intersection between the triangles corresponding to u and v is the same point as the intersection between the triangles corresponding to f and g. We prove that every 3-connected planar map admits a primal?Cdual contact representation by triangles. Moreover, the interiors of the triangles form a tiling of the triangle corresponding to the outer face and each contact point is a corner of exactly three triangles. Then we show that these representations are in one-to-one correspondence with generalized Schnyder woods defined by Felsner for 3-connected planar maps. 相似文献
16.
Christos A. Athanasiadis 《Annals of Combinatorics》2012,16(3):421-448
Face numbers of triangulations of simplicial complexes were studied by Stanley by use of his concept of a local h-vector. It is shown that a parallel theory exists for cubical subdivisions of cubical complexes, in which the role of the h-vector of a simplicial complex is played by the (short or long) cubical h-vector of a cubical complex, defined by Adin, and the role of the local h-vector of a triangulation of a simplex is played by the (short or long) cubical local h-vector of a cubical subdivision of a cube. The cubical local h-vectors are defined in this paper and are shown to share many of the properties of their simplicial counterparts. Generalizations to subdivisions of locally Eulerian posets are also discussed. 相似文献
17.
Carsten Thomassen 《Journal of Combinatorial Theory, Series B》1980,29(2):244-271
We present a short proof of the following theorems simultaneously: Kuratowski's theorem, Fary's theorem, and the theorem of Tutte that every 3-connected planar graph has a convex representation. We stress the importance of Kuratowski's theorem by showing how it implies a result of Tutte on planar representations with prescribed vertices on the same facial cycle as well as the planarity criteria of Whitney, MacLane, Tutte, and Fournier (in the case of Whitney's theorem and MacLane's theorem this has already been done by Tutte). In connection with Tutte's planarity criterion in terms of non-separating cycles we give a short proof of the result of Tutte that the induced non-separating cycles in a 3-connected graph generate the cycle space. We consider each of the above-mentioned planarity criteria for infinite graphs. Specifically, we prove that Tutte's condition in terms of overlap graphs is equivalent to Kuratowski's condition, we characterize completely the infinite graphs satisfying MacLane's condition and we prove that the 3-connected locally finite ones have convex representations. We investigate when an infinite graph has a dual graph and we settle this problem completely in the locally finite case. We show by examples that Tutte's criterion involving non-separating cycles has no immediate extension to infinite graphs, but we present some analogues of that criterion for special classes of infinite graphs. 相似文献
18.
Waldspurger's Involution and Types 总被引:1,自引:0,他引:1
Waldspurger's involution for the genuine irreducible supercuspidalrepresentations of SL2(F) is parametrized in terms of typesin the case F p-adic with p odd. In particular, it is shownthat the in-volution is given by conjugating by an element ofGL2(F) and twisting one of the defining parameters of an associatedtype by a quadratic character, the relevant parameter beinga character on the norm one elements of a quadratic extension. 相似文献
19.
Peter Damaschke 《Journal of Graph Theory》1990,14(4):427-435
We study classes of finite, simple, undirected graphs that are (1) lower ideals (or hereditary) in the partial order of graphs by the induced subgraph relation ≤i, and (2) well-quasi-ordered (WQO) by this relation. The main result shows that the class of cographs (P4-free graphs) is WQO by ≤i, and that this is the unique maximal lower ideal with one forbidden subgraph that is WQO. This is a consequence of the famous Kruskal theorem. Modifying our idea we can prove that P4-reducible graphs build a WQO class. Other examples of lower ideals WQO by ≤i are also given. 相似文献
20.
A set A in a metric space is called totally bounded if for each ε>0 the set can be ε-approximated by a finite set. If this can be done, the finite set can always be chosen inside A. If the finite sets are replaced by an arbitrary approximating family of sets, this coincidence may disappear. We present necessary and sufficient conditions for the coincidence assuming only that the family is closed under finite unions. A complete analysis of the structure of totally bounded sets is presented in the case that the approximating family is a bornology, where approximation in either sense amounts to approximation in Hausdorff distance by members of the bornology. 相似文献