A short proof of Gromov's filling inequality

DOI10.1090/S0002-9939-08-09203-4zbMath1148.53031arXivmath/0703889MaRDI QIDQ3518254

Stefan Wenger

Publication date: 7 August 2008

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0703889

zbMATH Keywords

isoperimetric inequalityLipschitz chainssystolic inequality

Mathematics Subject Classification ID

Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Related Items

Filling metric spaces, Systolic inequalities and minimal hypersurfaces, Filling inequalities for nilpotent groups through approximations., Isoperimetry of nilpotent groups, Regular geometric cycles, Relative systoles of relative-essential 2-complexes, Composing and decomposing surfaces and functions, Linear bounds for constants in Gromov's systolic inequality and related results, Volumes of balls in Riemannian manifolds and Uryson width, Lipschitz connectivity and filling invariants in solvable groups and buildings., Filling inequalities do not depend on topology, Dirac and Plateau billiards in domains with corners, Homological and homotopical Dehn functions are different, Rectifiability of flat chains in Banach spaces with coefficients in \(\mathbb Z_p\), Singularities, expanders and topology of maps. II: From combinatorics to topology via algebraic isoperimetry, Hurwitz quaternion order and arithmetic Riemann surfaces, Filling functions of arithmetic groups, Short geodesic loops on complete Riemannian manifolds with a finite volume, The growth of the first non-Euclidean filling volume function of the quaternionic Heisenberg group, Homological filling functions with coefficients

Cites Work

• Filling Riemannian manifolds
• Isoperimetric inequalities of Euclidean type in metric spaces
• Rectifiable Metric Spaces: Local Structure and Regularity of the Hausdorff Measure
• Currents in metric spaces