publication . Article . Preprint . 2004

A GENERALIZED AFFINE ISOPERIMETRIC INEQUALITY

Gaoyong Zhang; Deane Yang; Ralph Howard; Wenxiong Chen; Erwin Lutwak;
Open Access
  • Published: 05 Feb 2004 Journal: Journal of Geometric Analysis, volume 14, pages 597-612 (issn: 1050-6926, eissn: 1559-002X, Copyright policy)
  • Publisher: Springer Science and Business Media LLC
Abstract
A purely analytic proof is given for an inequality that has as a direct consequence the two most important affine isoperimetric inequalities of plane convex geometry: The Blaschke-Santalo inequality and the affine isoperimetric inequality of affine differential geometry.
Subjects
arXiv: Mathematics::Metric GeometryMathematics::Differential Geometry
free text keywords: Geometry and Topology, Mathematics - Metric Geometry, Mathematics - Classical Analysis and ODEs, 52A40 (Primary) 52A10 53A15 (Secondary), Mathematical analysis, Isoperimetric inequality, Pure mathematics, Affine transformation, Affine geometry of curves, Affine geometry, Affine differential geometry, Isoperimetric dimension, Linear inequality, Mathematics, Kantorovich inequality
Funded by
NSF| Isoperimetric Inequalities
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 0104363
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
,
NSF| Nonlinear PDEs in Geometric Analysis
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 0072328
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
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