A Gap Theorem for Free Boundary Minimal Surfaces in Geodesic Balls of Hyperbolic Space and Hemisphere

Haizhong Li; Changwei Xiong

doi:10.1007/s12220-017-9953-6

A Gap Theorem for Free Boundary Minimal Surfaces in Geodesic Balls of Hyperbolic Space and Hemisphere

Haizhong Li, Changwei Xiong^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

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.

Original language	English
Pages (from-to)	3171-3182
Number of pages	12
Journal	Journal of Geometric Analysis
Volume	28
Issue number	4
DOIs	https://doi.org/10.1007/s12220-017-9953-6
Publication status	Published - 15 Dec 2018

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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.",

keywords = "Free boundary, Gap theorem, Hemisphere, Hyperbolic space, Minimal surface",

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AU - Li, Haizhong

AU - Xiong, Changwei

PY - 2018/12/15

Y1 - 2018/12/15

N2 - 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.

AB - 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.

KW - Free boundary

KW - Gap theorem

KW - Hemisphere

KW - Hyperbolic space

KW - Minimal surface

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DO - 10.1007/s12220-017-9953-6

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JO - Journal of Geometric Analysis

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A Gap Theorem for Free Boundary Minimal Surfaces in Geodesic Balls of Hyperbolic Space and Hemisphere

Abstract

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