Rectifiability of planes and Alberti representations

Guy C. David, Bruce Kleiner

Research output: Contribution to journalArticle

Abstract

We study metric measure spaces that have quantitative topological control, as well as a weak form of differentiable structure. In particular, let X be a pointwise doubling metric measure space. Let U be a Borel subset on which the blowups of X are topological planes. We show that U can admit at most 2 independent Alberti representations. Furthermore, if U admits 2 Alberti representations, then the restriction of the measure to U is 2-rectifiable. This is a partial answer to the case n = 2 of a question of the second author and Schioppa.

Original languageEnglish (US)
Pages (from-to)723-756
Number of pages34
JournalAnnali della Scuola Normale Superiore di Pisa - Classe di Scienze
Volume19
Issue number2
DOIs
StatePublished - Jan 1 2019

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Rectifiability
Metric Measure Space
Doubling
Differentiable
Restriction
Partial
Subset
Form

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Mathematics (miscellaneous)

Cite this

Rectifiability of planes and Alberti representations. / David, Guy C.; Kleiner, Bruce.

In: Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Vol. 19, No. 2, 01.01.2019, p. 723-756.

Research output: Contribution to journalArticle

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