Semmes surfaces and intrinsic Lipschitz graphs in the Heisenberg group

Autor:	Fässler, Katrin, Orponen, Tuomas, Rigot, Séverine
Rok vydání:	2018
Předmět:	Mathematics - Classical Analysis and ODEs Mathematics - Metric Geometry 28A75 (Primary) 28A78 (Secondary)
Druh dokumentu:	Working Paper
Popis:	A Semmes surface in the Heisenberg group is a closed set $S$ that is upper Ahlfors-regular with codimension one and satisfies the following condition, referred to as Condition B. Every ball $B(x,r)$ with $x \in S$ and $0 < r < \operatorname{diam} S$ contains two balls with radii comparable to $r$ which are contained in different connected components of the complement of $S$. Analogous sets in Euclidean spaces were introduced by Semmes in the late $80$'s. We prove that Semmes surfaces in the Heisenberg group are lower Ahlfors-regular with codimension one and have big pieces of intrinsic Lipschitz graphs. In particular, our result applies to the boundary of chord-arc domains and of reduced isoperimetric sets. Comment: 39 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1803.04819 Zobrazit plný text záznamu View this record from Arxiv