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- W1978034458 abstract "We discuss the global regularity for 2 dimensional minimal sets that are near a $T$ set, that is, whether every global minimal set in $R^n$ that looks like a $T$ set at infinity is a $T$ set or not. The main point is to use the topological properties of a minimal set at large scale to control its topology at smaller scales. This is the idea to prove that all 1-dimensional Almgren-minimal sets in $R^n$, and all 2-dimensional Mumford-Shah minimal sets in $R^3$ are cones. In this article we discuss two types of 2-dimensional minimal sets: Almgren-minimal set in $R^3$ whose blow-in limit is a $T$ set; topological minimal sets in $R^4$ whose blow-in limit is a $T$ set. For the first one we eliminate an existing potential counterexample that was proposed by several people, and show that a real counterexample should have a more complicated topological structure; for the second we construct a potential example using a Klein bottle." @default.
- W1978034458 created "2016-06-24" @default.
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- W1978034458 date "2011-12-15" @default.
- W1978034458 modified "2023-09-27" @default.
- W1978034458 title "Global regularity for minimal sets near a $T$ set and counterexamples" @default.
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