共查询到20条相似文献,搜索用时 31 毫秒
1.
Ulrich Dierkes Dirk Schwab 《Calculus of Variations and Partial Differential Equations》2005,22(2):173-184
We construct quadratic forms on
which are subharmonic on any n-dimensional minimal submanifold in
and, more generally, on submanifolds of bounded mean curvature. This leads to nonexistence results for connected n-dimensional minimal submanifolds in
as well as to necessary conditions for the existence of connected submanifolds of bounded mean curvature with arbitrary codimension. Furthermore we discuss a barrier principle for n-dimensional submanifolds in
of bounded mean curvature.Received: 11 November 2003, Accepted: 29 January 2004, Published online: 2 April 2004Mathematics Subject Classification (2000):
35J60, 49Q05, 53C42 相似文献
2.
Weakly n-dimensional spaces were first distinguished by Karl Menger. In this note we shall discuss three topics concerning this class
of spaces: universal spaces, products, and the sum theorem. We prove that there is a universal space for the class of all
weakly n-dimensional spaces, present a simpler proof of Tomaszewski’s result about the dimension of a product of weakly n-dimensional spaces, and show that there is an n-dimensional space which admits a pairwise disjoint countable closed cover by weakly n-dimensional subspaces but is not weakly n-dimensional itself.
(Received 17 August 2000) 相似文献
3.
Christian Bär 《Inventiones Mathematicae》1999,138(1):183-202
Consider a nontrivial smooth solution to a semilinear elliptic system of first order with smooth coefficients defined over
an n-dimensional manifold. Assume the operator has the strong unique continuation property. We show that the zero set of the solution
is contained in a countable union of smooth (n−2)-dimensional submanifolds. Hence it is countably (n−2)-rectifiable and its Hausdorff dimension is at most n−2. Moreover, it has locally finite (n−2)-dimensional Hausdorff measure. We show by example that every real number between 0 and n−2 actually occurs as the Hausdorff dimension (for a suitable choice of operator). We also derive results for scalar elliptic
equations of second order.
Oblatum 22-V-1998 & 26-III-1999 / Published online: 10 June 1999 相似文献
4.
Weakly n-dimensional spaces were first distinguished by Karl Menger. In this note we shall discuss three topics concerning this class of spaces: universal spaces, products, and the sum theorem. We prove that there is a universal space for the class of all weakly n-dimensional spaces, present a simpler proof of Tomaszewski’s result about the dimension of a product of weakly n-dimensional spaces, and show that there is an n-dimensional space which admits a pairwise disjoint countable closed cover by weakly n-dimensional subspaces but is not weakly n-dimensional itself. 相似文献
5.
In this note we show that the (n−2)-dimensional volumes of codimension 2 faces of an n-dimensional simplex are algebraically independent quantities of the volumes of its edge-lengths. The proof involves computation
of the eigenvalues of Kneser graphs. We also show examples of families of simplices (of dimension 4 or greater) which show
that the set of (n−2)-dimensional volumes of (n−2)-dimensional faces of a simplex do not determine its volume. 相似文献
6.
Philippe Rukimbira 《Annals of Global Analysis and Geometry》1994,12(1):103-108
For K-contact flows on (2n+1)-dimensional compact manifolds, we show that the dimension of any leaf closure is at most the smaller of (n+1) and 2n+1) minus the rank of the vector space of harmonic vector fields. 相似文献
7.
Onur Alper 《纯数学与应用数学通讯》2020,73(4):855-915
We study the singular set of free interface in an optimal partition problem for the Dirichlet eigenvalues. We prove that its upper (n − 2) -dimensional Minkowski content, and consequently its (n − 2) -dimensional Hausdorff measure, are locally finite. We also show that the singular set is countably (n − 2) -rectifiable; namely, it can be covered by countably many C1 -manifolds of dimension (n − 2) , up to a set of (n − 2) -dimensional Hausdorff measure zero. Our results hold for optimal partitions on Riemannian manifolds and harmonic maps into homogeneous trees as well. © 2019 Wiley Periodicals, Inc. 相似文献
8.
Yoshinobu Kamishima 《Geometriae Dedicata》2006,122(1):33-49
Long and Reid [Algebr. Geom. Topol. 2: 285–296, 2002] have shown that the diffeomorphism class of every Riemannian flat manifold
of dimension n≥ 3 arises as a cusp cross-section of a complete finite volume real hyperbolic (n+1)-orbifold. For the complex hyperbolic case, McReynolds [Algebr. Geom. Topol. 4: 721–755, 2004] proved that every 3-dimensional
infranilmanifold is diffeomorphic to a cusp cross-section of a complete finite volume complex hyperbolic 2-orbifold. Moreover,
he gave a necessary and sufficient condition for a Heisenberg infranilmanifold to be realized as a cusp cross-section of finite
volume (arithmetically) complex hyperbolic orbifold. We study these realization problems by using Seifert fibrations. 相似文献
9.
We show that for any differentiable involution on anr-dimensional manifold (M, T) whose fixed point setF is a disjoint union of real projective spaces of constant dimension 2n, we have: ifr=4n then (M,T) is bordant to (F×F, twist), if 2n<r4n then (M,T) bounds. 相似文献
10.
11.
Xiantao Wang 《Mathematische Zeitschrift》2003,243(4):643-651
We will derive a new discreteness condition for n-dimensional M?bius subgroups as well as obtain some results concerning classification of such groups. We will also discuss
dense subgroups of n-dimensional M?bius groups. The main result is that any dense group of an n-dimensional M?bius group contains a dense subgroup which is generated by at most n elements if .
Received: 5 June 2001 / Published online: 24 February 2003
RID="*"
ID="*" The research was partly supported by FNS of China, grant number 19801011 相似文献
12.
We present a generalization of the mixed integer rounding (MIR) approach for generating valid inequalities for (mixed) integer
programming (MIP) problems. For any positive integer n, we develop n facets for a certain (n + 1)-dimensional single-constraint polyhedron in a sequential manner. We then show that for any n, the last of these facets (which we call the n-step MIR facet) can be used to generate a family of valid inequalities for the feasible set of a general (mixed) IP constraint, which we
refer to as the n-step MIR inequalities. The Gomory Mixed Integer Cut and the 2-step MIR inequality of Dash and günlük (Math Program 105(1):29–53, 2006) are the
first two families corresponding to n = 1,2, respectively. The n-step MIR inequalities are easily produced using periodic functions which we refer to as the n-step MIR functions. None of these functions dominates the other on its whole period. Finally, we prove that the n-step MIR inequalities generate two-slope facets for the infinite group polyhedra, and hence are potentially strong.
相似文献
13.
In an earlier paper the second author used the formal, algebraicproperties of 2-dimensional Shintani generating functions toconstruct a 1-cocycle on PGL2{Q}. We aim to generalise theseresults by using such functions in dimension n to obtain an(n1)-cocycle on PGLn{Q}, presumably related to the Bernoulliand Eisenstein cocycles of R. Sczech. By improving our methodswe achieve this goal for n=3. For n>3 we encounter obstaclesrelated to degenerate configurations of hyperplanes in n-space.Nevertheless, we obtain partial results closely connected toreciprocity laws for certain n-dimensional Dedekind sums. 1991Mathematics Subject Classification: 11F20, 11F75. 相似文献
14.
We denote by ℳ
R
n
the test neighbourhood sufficient to extract the Euclidean Medial Axis of any n-dimensional discrete shape whose inner radius is no greater than R. In this paper, we study properties of discrete Euclidean disks overlappings so as to prove that in any given dimension n, ℳ
R
n
tends to the set of visible vectors as R tends to infinity. 相似文献
15.
I. P. Chukhrov 《Journal of Applied and Industrial Mathematics》2012,6(1):42-55
Studying the extreme kernel face complexes of a given dimension, we obtain some lower estimates of the number of shortest
face complexes in the n-dimensional unit cube. The number of shortest complexes of k-dimensional faces is shown to be of the same logarithm order as the number of complexes consisting of at most 2
n−1 different k-dimensional faces if 1 ≤ k ≤ c · n and c < 0.5. This implies similar lower bounds for the maximum length of the kernel DNFs and the number of the shortest DNFs of
Boolean functions. 相似文献
16.
We show how to construct the group using any sequence of Hadamard matrices. This construction is nicely compatible with the
classical Haar and Rademacher functions. We then show that every
n-dimensional Euclidean lattice is isometrically
isomorphic to a n-slice of .
Finally we prove a similar embedding theorem for integral and p-rational lattices into the-module of all continuous
integer-valued functions on the group of p-adic integers.
Received 29 October 2001. 相似文献
17.
We establish compactness of solutions to the Yamabe problem on any smooth compact connected Riemannian manifold (not conformally diffeomorphic to standard spheres) of dimension n?7 as well as on any manifold of dimension n?8 under some additional hypothesis. To cite this article: Y.Y. Li, L. Zhang, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
18.
Given an arbitrary n, we consider anisotropic quadratic forms of dimension n over all fields of characteristic ≠ 2 and prove that the height of an n-dimensional excellent form (depending on n only) is the (precise) lower bound of the heights of all forms of dimension n.
The second and third authors were partially supported by the European Community’s Human Potential Programme under contract
HPRN-CT-2002-00287, KTAGS. The James D.Wolfensohn Fund and The Ellentuck Fund support is acknowledged by the second author.
Received: 9 December 2005 相似文献
19.
Vandermonde Matrices, NP-Completeness, and Transversal Subspaces 总被引:1,自引:0,他引:1
Alexander Chistov Hervé Fournier Leonid Gurvits Pascal Koiran 《Foundations of Computational Mathematics》2003,3(4):421-427
Let K be an infinite field. We give polynomial time constructions of families of r-dimensional subspaces of K
n
with the following transversality property: any linear subspace of K
n
of dimension n–r is transversal to at least one element of the family. We also give a new NP-completeness proof for the following problem: given two integers n and m with n \leq m and a n × m matrix A with entries in Z, decide whether there exists an n × n subdeterminant of A which is equal to zero. 相似文献
20.
A. V. Isaev 《Proceedings of the Steklov Institute of Mathematics》2006,253(1):225-245
We survey our recent classification results for Kobayashi-hyperbolic n-dimensional manifolds with holomorphic automorphism group of dimension at least n
2 − 1 for n ≥ 2. 相似文献