Hilbert volume in metric spaces. Part 1

Misha Gromov

doi:10.2478/s11533-011-0143-7

Hilbert volume in metric spaces. Part 1

Misha Gromov

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce a notion of Hilbertian n-volume in metric spaces with Besicovitch-type inequalities built-in into the definitions. The present Part 1 of the article is, for the most part, dedicated to the reformulation of known results in our terms with proofs being reduced to (almost) pure tautologies. If there is any novelty in the paper, this is in forging certain terminology which, ultimately, may turn useful in an Alexandrov kind of approach to singular spaces with positive scalar curvature [Gromov M., Plateau-hedra, Scalar Curvature and Dirac Billiards, in preparation].

Original language	English (US)
Pages (from-to)	371-400
Number of pages	30
Journal	Central European Journal of Mathematics
Volume	10
Issue number	2
DOIs	https://doi.org/10.2478/s11533-011-0143-7
State	Published - Apr 2012

Keywords

Besicovitch inequality
John's ellipsoid
Lipschitz maps
Riemannian volume

ASJC Scopus subject areas

General Mathematics

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10.2478/s11533-011-0143-7

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Hilbert volume in metric spaces. Part 1

Abstract

Keywords

ASJC Scopus subject areas

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