A Note on Cheeger’s Isoperimetric Constant

In this short exposition, we provide a simplified proof of Buser’s result for Cheeger’s isoperimetric constant. We also provide a comprehensive approach on how to obtain volume estimates for smooth hypersurfaces.

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Bibliographic Details
Published inThe Journal of geometric analysis Vol. 32; no. 11
Main Authors Charalambous, Nelia, Lu, Zhiqin
Format Journal Article
LanguageEnglish
Published New York Springer US 01.11.2022
Springer Nature B.V
Subjects
Abstract Harmonic Analysis
Analysis and Geometry of Complete Manifolds: A Special Issue in Honor of Peter Li
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Geometry
Global Analysis and Analysis on Manifolds
Hyperspaces
Mathematics
Mathematics and Statistics
Cheeger’s constant
Isoperimetric inequality
Primary: 53C21
Riccati equation
Mean curvature
Secondary: 58J60
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Summary:In this short exposition, we provide a simplified proof of Buser’s result for Cheeger’s isoperimetric constant. We also provide a comprehensive approach on how to obtain volume estimates for smooth hypersurfaces.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-022-01028-5