Topological minimal sets and their applications

Details Topological minimal sets and their applications Topological minimal sets and their applications

2011-03-20

arxiv.org/abs/1103.3871v1

Mathematics

Classical Analysis and ODEs

Scientific paper

In this article we introduce a definition of topological minimal sets, which is a generalization of that of Mumford-Shah-minimal sets. We prove some general properties as well as two existence theorems for topological minimal sets. As an application we prove the topological minimality of the union of two almost orthogonal planes in $\R^4$, and use it to improve the angle criterion under which the union of several higher dimensional planes is Almgren-minimal.

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