Displaying similar documents to “Equivalence of geometric and combinatorial Dehn functions.”

Hilbert volume in metric spaces. Part 1

Misha Gromov (2012)

Open Mathematics

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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...

Length of curves on Lip manifolds

Giuseppe De Cecco, Giuliana Palmieri (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In this paper the length of a curve on a Lipschitz Riemannian manifold is defined. It is shown that the above definition is consistent with the definition of the geodesic distance already introduced by the authors, both in a geometrical and analytical way.

Simplicial nonpositive curvature

Tadeusz Januszkiewicz, Jacek Świątkowski (2006)

Publications Mathématiques de l'IHÉS

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We introduce a family of conditions on a simplicial complex that we call local -largeness (≥6 is an integer). They are simply stated, combinatorial and easily checkable. One of our themes is that local 6-largeness is a good analogue of the non-positive curvature: locally 6-large spaces have many properties similar to non-positively curved ones. However, local 6-largeness neither implies nor is implied by non-positive curvature of the standard metric. One can think of these results as...