Hilbert volume in metric spaces. Part 1 |
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| Authors: | Misha Gromov |
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| Institution: | 1.Institut des Hautes études Scientifiques,Bures-sur-Yvette,France;2.Courant Institute of Mathematical Sciences,New York University,New York,USA |
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| 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]. |
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