The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension
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In this paper, it was proved that there exist no singular points in case m = 0.1.1, where m is a smooth m-dimensional submanifold of 2.Abstract:
1. When describing the interior structure of an area minimizing m dimensional locally rectifiable current T in jR, one calls a point #£sp t r ^ s p t dT regular or singular according to whether or not x has a neighborhood V such that VT\spt T is a smooth m dimensional submanifold of 2?. As a result of the efforts of many geometers it is known that there exist no singular points in case m ^ 6 ; a detailed exposition of this theory may be found in [3, Chapter 5]. Recently it was proved in [2] thatread more
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Asymptotics for a class of non-linear evolution equations, with applications to geometric problems
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References
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Book
Geometric Measure Theory
TL;DR: In this article, Grassmann algebras of a vectorspace have been studied in the context of the calculus of variations, and a glossary of some standard notations has been provided.
BookDOI
Multiple integrals in the calculus of variations
TL;DR: In this paper, a variational method in the theory of harmonic integrals has been proposed to solve the -Neumann problem on strongly pseudo-convex manifolds and parametric Integrals two-dimensional problems.
Journal ArticleDOI
Minimal Cones and the Bernstein Problem.
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