Relative volume comparison theorems in Finsler geometry and their applications

Document Type: Research Paper

Author

Department of Mathematics Minjiang University

Abstract

We establish some relative volume comparison theorems for extremal volume forms of‎ ‎Finsler manifolds under suitable curvature bounds‎. ‎As their applications‎, ‎we obtain some results on curvature and topology of Finsler manifolds‎. ‎Our results remove the usual assumption on S-curvature that is needed in the literature‎.

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Volume 40, Issue 1
January and February 2014
Pages 217-234
  • Receive Date: 01 March 2012
  • Revise Date: 03 January 2013
  • Accept Date: 03 January 2013