Systolic inequalities and minimal hypersurfaces

DOI10.1007/s00039-010-0052-0zbMath1185.53045arXiv0903.5299OpenAlexW2964320393WikidataQ59664721 ScholiaQ59664721MaRDI QIDQ2379373

Lawrence Guth

Publication date: 19 March 2010

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.5299

zbMATH Keywords

\(n\)-dimensional torus

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Related Items (19)

Filling metric spaces ⋮ Macroscopic band width inequalities ⋮ Macroscopic scalar curvature and areas of cycles ⋮ Bavard's systolically extremal Klein bottles and three dimensional applications ⋮ Relative systoles of relative-essential 2-complexes ⋮ Linear bounds for constants in Gromov's systolic inequality and related results ⋮ Hyperellipticity and systoles of Klein surfaces ⋮ Systoles and Dehn surgery for hyperbolic 3-manifolds ⋮ Bi-Lipschitz approximation by finite-dimensional imbeddings ⋮ Cohomological dimension, self-linking, and systolic geometry ⋮ Length product of homologically independent loops for tori ⋮ Hurwitz quaternion order and arithmetic Riemann surfaces ⋮ Unnamed Item ⋮ A Pu-Bonnesen inequality ⋮ The minimal length product over homology bases of manifolds ⋮ A systolic inequality with remainder in the real projective plane ⋮ Uryson width and volume ⋮ Convex programs for minimal-area problems ⋮ Waist of maps measured via Urysohn width

Cites Work

• Volumes of balls in large Riemannian manifolds
• Filling Riemannian manifolds
• On the structure of manifolds with positive scalar curvature
• A short proof of Gromov's filling inequality
• Incompressible minimal surfaces, three-dimensional manifolds with nonnegative scalar curvature, and the positive mass conjecture in general relativity
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu

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