Dehn functions and Hölder extensions in asymptotic cones

Alexander Lytchak, Stefan Wenger, Robert Young

Research output: Contribution to journalArticlepeer-review

Abstract

The Dehn function measures the area of minimal discs that fill closed curves in a space; it is an important invariant in analysis, geometry, and geometric group theory. There are several equivalent ways to define the Dehn function, varying according to the type of disc used. In this paper, we introduce a new definition of the Dehn function and use it to prove several theorems. First, we generalize the quasi-isometry invariance of the Dehn function to a broad class of spaces. Second, we prove Hölder extension properties for spaces with quadratic Dehn function and their asymptotic cones. Finally, we show that ultralimits and asymptotic cones of spaces with quadratic Dehn function also have quadratic Dehn function. The proofs of our results rely on recent existence and regularity results for area-minimizing Sobolev mappings in metric spaces.

Original languageEnglish (US)
Pages (from-to)79-109
Number of pages31
JournalJournal fur die Reine und Angewandte Mathematik
Volume2020
Issue number763
DOIs
StatePublished - Jun 1 2020

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Dehn functions and Hölder extensions in asymptotic cones'. Together they form a unique fingerprint.

Cite this