Semmes surfaces and intrinsic Lipschitz graphs in the Heisenberg group
| Autor: | Séverine Rigot, Katrin Fässler, Tuomas Orponen |
|---|---|
| Přispěvatelé: | University of Fribourg, University of Helsinki, Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), ANR-15-CE40-0018,SRGI,Géométrie sous-Riemannienne et Interactions(2015) |
| Rok vydání: | 2020 |
| Předmět: |
Closed set
Applied Mathematics General Mathematics 010102 general mathematics Boundary (topology) Metric Geometry (math.MG) Codimension Lipschitz continuity Surface (topology) 01 natural sciences Combinatorics 28A75 (Primary) 28A78 (Secondary) Mathematics - Metric Geometry Mathematics - Classical Analysis and ODEs Classical Analysis and ODEs (math.CA) FOS: Mathematics Heisenberg group Mathematics::Metric Geometry mittateoria [MATH]Mathematics [math] 0101 mathematics Isoperimetric inequality ComputingMilieux_MISCELLANEOUS Mathematics Complement (set theory) |
| Zdroj: | Transactions of the American Mathematical Society Transactions of the American Mathematical Society, American Mathematical Society, 2020, 373 (8), pp.5957-5996. ⟨10.1090/tran/8146⟩ |
| ISSN: | 1088-6850 0002-9947 |
| DOI: | 10.1090/tran/8146 |
| 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. 39 pages, 4 figures |
| Databáze: | OpenAIRE |
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