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A Universal Volume Comparison Theorem for Finsler Manifolds and Related Results

  Published:2012-10-30
 Printed: Dec 2013
  • Wei Zhao,
    Center of Mathematical Sciences, Zhejiang University, Hangzhou, China
  • Yibing Shen,
    Center of Mathematical Sciences, Zhejiang University, Hangzhou, China
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Abstract

In this paper, we establish a universal volume comparison theorem for Finsler manifolds and give the Berger-Kazdan inequality and Santaló's formula in Finsler geometry. Being based on these, we derive a Berger-Kazdan type comparison theorem and a Croke type isoperimetric inequality for Finsler manifolds.
Keywords: Finsler manifold, Berger-Kazdan inequality, Berger-Kazdan comparison theorem, Santaló's formula, Croke's isoperimetric inequality Finsler manifold, Berger-Kazdan inequality, Berger-Kazdan comparison theorem, Santaló's formula, Croke's isoperimetric inequality
MSC Classifications: 53B40, 53C65, 52A38 show english descriptions Finsler spaces and generalizations (areal metrics)
Integral geometry [See also 52A22, 60D05]; differential forms, currents, etc. [See mainly 58Axx]
Length, area, volume [See also 26B15, 28A75, 49Q20]
53B40 - Finsler spaces and generalizations (areal metrics)
53C65 - Integral geometry [See also 52A22, 60D05]; differential forms, currents, etc. [See mainly 58Axx]
52A38 - Length, area, volume [See also 26B15, 28A75, 49Q20]
 

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