Hilbert volume in metric spaces. Part 1

Misha Gromov

Open Mathematics (2012)

  • Volume: 10, Issue: 2, page 371-400
  • ISSN: 2391-5455

Abstract

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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].

How to cite

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Misha Gromov. "Hilbert volume in metric spaces. Part 1." Open Mathematics 10.2 (2012): 371-400. <http://eudml.org/doc/269311>.

@article{MishaGromov2012,
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].},
author = {Misha Gromov},
journal = {Open Mathematics},
keywords = {Riemannian volume; Lipschitz maps; Besicovitch inequality; John’s ellipsoid; John's ellipsoid},
language = {eng},
number = {2},
pages = {371-400},
title = {Hilbert volume in metric spaces. Part 1},
url = {http://eudml.org/doc/269311},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Misha Gromov
TI - Hilbert volume in metric spaces. Part 1
JO - Open Mathematics
PY - 2012
VL - 10
IS - 2
SP - 371
EP - 400
AB - 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].
LA - eng
KW - Riemannian volume; Lipschitz maps; Besicovitch inequality; John’s ellipsoid; John's ellipsoid
UR - http://eudml.org/doc/269311
ER -

References

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