A Gap Theorem for Free Boundary Minimal Surfaces in Geodesic Balls of Hyperbolic Space and Hemisphere |
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| Authors: | Haizhong Li Changwei Xiong |
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| Institution: | 1.Department of Mathematical Sciences,Tsinghua University,Beijing,People’s Republic of China;2.Mathematical Sciences Institute,Australian National University,Canberra, ACT,Australia |
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| Abstract: | In this paper we provide a pinching condition for the characterization of the totally geodesic disk and the rotational annulus among minimal surfaces with free boundary in geodesic balls of three-dimensional hyperbolic space and hemisphere. The pinching condition involves the length of the second fundamental form, the support function of the surface, and a natural potential function in hyperbolic space and hemisphere. |
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