2021/03/02 by Mengqing Zhan, Linfeng Zhou 路 1 citation
Physics and Astronomy 路 Mathematics 路 #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows
paper 路 doi:10.1090/proc/14959
This paper is a continuation of the second author鈥檚 previous work [Internat. J. Math. 30 (2019)]. We investigate the isoperimetric problem in the 2-dimensional Finsler space form <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis upper F Subscript upper B Baseline comma upper B squared left-parenthesis 1 right-parenthesis right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mi>F</mml:mi> <mml:mi>B</mml:mi> </mml:msub> <mml:mo>,</mml:mo> <mml:msup> <mml:mi>B</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">(FB, B2(1))</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k equals 0"> <mml:semantics> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">k=0</mml:annotation> </mml:semantics> </mml:math> </inline-formula> by using the Holmes-Thompson area and prove that the circle centered at the origin achieves the local maximum area of the isoperimetric problem.