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A Universal Volume Comparison Theorem for Finsler Manifolds and Related Results

Published online by Cambridge University Press:  20 November 2018

Wei Zhao  and
Yibing Shen
Wei Zhao
Affiliation:
Center of Mathematical Sciences, Zhejiang University, Hangzhou, China, e-mail: [email protected], [email protected]
Yibing Shen
Affiliation:
Center of Mathematical Sciences, Zhejiang University, Hangzhou, China, e-mail: [email protected], [email protected]
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Abstract

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In this paper, we establish a universal volume comparison theorem for Finsler manifolds and give the Berger–Kazdan inequality and Santalá's formula in Finsler geometry. Based on these, we derive a Berger–Kazdan type comparison theorem and a Croke type isoperimetric inequality for Finsler manifolds.

Keywords

53B4053C6552A38Finsler manifoldBerger–Kazdan inequalityBerger–Kazdan comparison theoremSantalá's formulaCroke's isoperimetric inequality
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 65 , Issue 6 , 01 December 2013 , pp. 1401 - 1435
Copyright
Copyright © Canadian Mathematical Society 2013

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