Minimal volume with length bounded below

DOI10.1016/j.difgeo.2005.01.005zbMath1077.53036OpenAlexW2046663019WikidataQ115357982 ScholiaQ115357982MaRDI QIDQ558082

Neil N. Katz

Publication date: 30 June 2005

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.difgeo.2005.01.005

zbMATH Keywords

integral geometryfilling volumeisosystolic inequalities

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Integral geometry (53C65) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Cites Work

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• Rigidity and the distance between boundary points
• Filling Riemannian manifolds
• Inégalité isosystolique pour la bouteille de Klein. (Isosystolic inequalities for the Klein bottle)
• Inégalités isosystoliques conformes pour la bouteille de Klein. (Conformal isosystolic inequalities for the Klein bottle)
• Revolution metrics of a disc and rotation invariance of the length of geodesics
• On the length of the geodesics of a metric of negative curvature on the disc.
• Solvability of the integral geometry problem for geodesics
• Isosystolic conformal inequalities
• Filling area conjecture and ovalless real hyperelliptic surfaces
• A Proof of the Isosystolic Inequality for the Klein Bottle
• Local boundary rigidity of a compact Riemannian manifold with curvature bounded above
• Equivalent Norms for Sobolev Spaces
• An exact sequence in differential topology
• Integral geometry of a tensor field on a manifold whose curvature is bounded above

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