Improvement and generalisation of Papasoglu's lemma
Simon Allais
TL;DR
This paper enhances an existing isoperimetric inequality by Papasoglu and extends it to the Finsler geometry setting, providing a more general and optimal version applicable to various Finsler volumes.
Contribution
It introduces a generalized and optimal Finsler version of Papasoglu's lemma, broadening its applicability in geometric analysis.
Findings
Improved the original isoperimetric inequality of Papasoglu.
Generalized the inequality to the Finsler geometric context.
Proved an optimal Finsler version of Besicovitch's lemma.
Abstract
We improve an isoperimetric inequality due to Panos Papasoglu. We also generalize this inequality to the Finsler case by proving an optimal Finsler version of the Besicovitch's lemma which holds for any notion of Finsler volume.
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Taxonomy
TopicsAdvanced Differential Geometry Research · Geometric Analysis and Curvature Flows · Dermatological and Skeletal Disorders