Abstract
The isoperimetric problem is one of the fundamental problems in differential geometry. By using the method of the calculus of variations we show that the circle centered at the origin in \({\mathbb {B}}^2(1)\) is a proper maximum of the isoperimetric problem in a 2-dimensional Finsler space of Funk type. We also obtain the formula of area enclosed by a simple closed curve in a spherically symmetric Finsler plane.
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Acknowledgements
This paper has benefitted from our discussions with Professor Linfeng Zhou. The authors are grateful to the referee for his careful reading of the manuscript and very helpful suggestions.
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Supported by the National Natural Science Foundation of China 11371032.
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Li, Y., Mo, X. On Isoperimetric Problem in a 2-Dimensional Finsler Space of Funk type. Results Math 75, 154 (2020). https://doi.org/10.1007/s00025-020-01282-5
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DOI: https://doi.org/10.1007/s00025-020-01282-5