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991.
Minimal Surfaces in the Heisenberg Group 总被引:9,自引:0,他引:9
Scott D. Pauls 《Geometriae Dedicata》2004,104(1):201-231
We investigate the minimal surface problem in the three dimensional Heisenberg group, H, equipped with its standard Carnot–Carathéodory metric. Using a particular surface measure, we characterize minimal surfaces in terms of a sub-elliptic partial differential equation and prove an existence result for the Plateau problem in this setting. Further, we provide a link between our minimal surfaces and Riemannian constant mean curvature surfaces in H equipped with different Riemannian metrics approximating the Carnot–Carathéodory metric. We generate a large library of examples of minimal surfaces and use these to show that the solution to the Dirichlet problem need not be unique. Moreover, we show that the minimal surfaces we construct are in fact X-minimal surfaces in the sense of Garofalo and Nhieu. 相似文献
992.
Doug Pickrell 《Journal of Functional Analysis》2006,234(2):321-363
Let X denote a simply connected compact Riemannian symmetric space, U the universal covering of the identity component of the group of automorphisms of X, and LU the loop group of U. In this paper we prove the existence (and conjecture the uniqueness) of an LU-invariant probability measure on a distributional completion of the loop space of X. 相似文献
993.
Sami Mustapha 《Journal of Theoretical Probability》2006,19(4):773-787
It is shown in this paper that the transition kernels corresponding to simple random walks on certain unimodular solvable
p-adic groups admit upper Gaussian estimates.
相似文献
994.
We give an overview of zero-sum theory in finite abelian groups, a subfield of additive group theory and combinatorial number theory. In doing so we concentrate on the algebraic part of the theory and on the development since the appearance of the survey article by Y. Caro in 1996. 相似文献
995.
Braid cryptosystem was proposed in CRYPTO 2000 as an alternate public-key cryptosystem. The security of this system is based
upon the conjugacy problem in braid groups. Since then, there have been several attempts to break the braid cryptosystem by
solving the conjugacy problem in braid groups. In this article, we first survey all the major attacks on the braid cryptosystem
and conclude that the attacks were successful because the current ways of random key generation almost always result in weaker
instances of the conjugacy problem. We then propose several alternate ways of generating hard instances of the conjugacy problem
for use braid cryptography.
相似文献
996.
I. D. Suprunenko 《Acta Appl Math》1998,52(1-3):325-330
The minimal polynomials of images of unipotent elements in irreducible rational representations of a special linear group over an algebraically closed field of characteristic p > 2 are found. In particular, we show that the degree of such polynomial is equal to the order of an element provided the highest weight of a representation is in some sense large enough with respect to p. 相似文献
997.
We present a general condition, based on the idea of n-generating subgroup sets, which implies that a given character represents a point in the homotopical or homological -invariants of the group G. Let be a finite simplicial graph, the flag complex induced by , and the graph group, or 'right angled Artin group', defined by . We use our result on n-generating subgroup sets to describe the homotopical and homological -invariants of in terms of the topology of subcomplexes of . In particular, this work determines the finiteness properties of kernels of maps from graph groups to abelian groups. This
is the first complete computation of the -invariants for a family of groups whose higher invariants are not determined - either implicitly or explicitly - by
1.
Received: October 18, 1996 相似文献
998.
We study the geometrical meaning of the Faà di Bruno polynomials in the context of KP theory. They provide a basis in a subspace W of the universal Grassmannian associated to the KP hierarchy. When W comes from geometrical data via the Krichever map, the Faà di Bruno recursion relation turns out to be the cocycle condition for (the Welters hypercohomology group describing) the deformations of the dynamical line bundle on the spectral curve together with the meromorphic sections which give rise to the Krichever map. Starting from this, one sees that the whole KP hierarchy has a similar cohomological meaning. 相似文献
999.
B. A. Rosenfeld 《Acta Appl Math》1998,50(1-2):103-110
In this paper the geometric interpretation of the exceptional Lie groups F4, E6, E7, and E8 is given. These groups are groups of motions of elliptic hyperbolic planes over nonassociative algebras of octaves and split octaves and their tensor products with algebras of usual and split complex numbers, quaternions and octaves. The explicit expressions of motions of these planes and their figures of symmetry are presented. 相似文献
1000.
Enrico Leuzinger 《Differential Geometry and its Applications》2004,20(3):141-318
The results in this paper are based on a previously constructed exhaustion of a locally symmetric space V=ΓX by Riemannian polyhedra, i.e., compact submanifolds with corners: V=s0V(s). We show that the interior of every polyhedron V(s) is homeomorphic to V. The universal covering space X(s) of V(s) is quasi-isometric to the discrete group Γ. It can be written as the complement of a Γ-invariant union of horoballs in X (which in general have intersections giving rise to the corners). This yields exponential isoperimetric inequalities for Γπ1(V(s)). We also discuss the relation of this compactification of V with the Borel–Serre compactification. 相似文献