Results 11 to 20 of about 328 (30)
Filling inequalities do not depend on topology [PDF]
, 2008 Gromov's universal filling inequalities relate the filling radius and the filling volume of a Riemannian manifold to its volume. The main result of the present article is that in dimensions at least three the optimal constants in the filling inequalities
Brunnbauer, Michael
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Small values of the Lusternik-Schnirelmann category for manifolds [PDF]
, 2007 We prove that manifolds of Lusternik-Schnirelmann category 2 necessarily have free fundamental group. We thus settle a 1992 conjecture of Gomez-Larranaga and Gonzalez-Acuna, by generalizing their result in dimension 3, to all higher dimensions.
Dranishnikov, Alexander N. +2 more
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Local extremality of the Calabi-Croke sphere for the length of the shortest closed geodesic [PDF]
, 2009 Recently, F. Balacheff proved that the Calabi-Croke sphere made of two flat 1-unit-side equilateral triangles glued along their boundaries is a local extremum for the length of the shortest closed geodesic among the Riemannian spheres with conical ...
Sabourau, Stephane
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Growth of quotients of groups acting by isometries on Gromov hyperbolic spaces [PDF]
, 2012 We show that every non-elementary group $G$ acting properly and cocompactly by isometries on a proper geodesic Gromov hyperbolic space $X$ is growth tight. In other words, the exponential growth rate of $G$ for the geometric (pseudo)-distance induced by $
Sabourau, Stephane
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A note on the Almost Schur lemma on smooth metric measure spaces
, 2018 In this paper, we prove almost Schur Lemma on closed smooth metric measure spaces, which implies the results of X.
Chen, Jui-Tang
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Bounded characteristic classes and flat bundles
, 2012 Let G be a connected Lie group, G^d the underlying discrete group, and BG, BG^d their classifying spaces. Let R denote the radical of G. We show that all classes in the image of the canonical map in cohomology H^*(BG,R)->H^*(BG^d,R) are bounded if and ...
Chatterji, Indira +3 more
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Enlargeable metrics on nonspin manifolds
, 2019 We show that an enlargeable Riemannian metric on a (possibly nonspin) manifold cannot have uniformly positive scalar curvature. This extends a well-known result of Gromov and Lawson to the nonspin setting.
Cecchini, Simone, Schick, Thomas
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A parametrized compactness theorem under bounded Ricci curvature
, 2017 We prove a parametrized compactness theorem on manifolds of bounded Ricci curvature, upper bounded diameter and lower bounded injectivity radius.Comment: 17 pages. Final version to appear in Front. Math. China. Reformulation of Theorem B to Corollary 1,
Li, Xiang, Xu, Shicheng
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On the metric compactification of infinite-dimensional $\ell_{p}$ spaces
, 2018 The notion of metric compactification was introduced by Gromov and later rediscovered by Rieffel; and has been mainly studied on proper geodesic metric spaces.
Gutiérrez, Armando W.
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Filling area conjecture and ovalless real hyperelliptic surfaces
, 2004 We prove the filling area conjecture in the hyperelliptic case. In particular, we establish the conjecture for all genus 1 fillings of the circle, extending P. Pu's result in genus 0.
Bangert, Victor +3 more
core +3 more sources