The isoperimetric problem in the 2-dimensional Finsler space forms with 𝑘=0. II-Reference-Cited by-同舟云学术

The isoperimetric problem in the 2-dimensional Finsler space forms with 𝑘=0. II

Published:2021-03-02 Issue:5 Volume:149 Page:2187-2198
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Zhan Mengqing,Zhou Linfeng

Abstract

This paper is a continuation of the second author’s previous work [Internat. J. Math. 30 (2019)]. We investigate the isoperimetric problem in the 2-dimensional Finsler space form ( F B , B 2 ( 1 ) ) (F_B, B^2(1)) with k = 0 k=0 by using the Holmes-Thompson area and prove that the circle centered at the origin achieves the local maximum area of the isoperimetric problem.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

https://www.ams.org/proc/2021-149-05/S0002-9939-2021-14959-9/S0002-9939-2021-14959-9.pdf

Reference9 articles.

1. A class of Finsler metrics with isotropic 𝑆-curvature;Cheng, Xinyue;Israel J. Math.,2009

2. A sufficiency proof for isoperimetric problems in the calculus of variations;Hestenes, M. R.;Bull. Amer. Math. Soc.,1938

3. On the classification of projectively flat Finsler metrics with constant flag curvature;Li, Benling;Adv. Math.,2014

4. On a class of projectively flat Finsler metrics of negative constant flag curvature;Mo, Xiaohuan;Internat. J. Math.,2012

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