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Free boundary constant mean curvature surfaces in a strictly convex three-manifold

Authors
Min, Sung-HongSeo, Keomkyo
Issue Date
Apr-2022
Publisher
SPRINGER
Keywords
Free boundary; Constant mean curvature; Spherical cap; Delaunay surface; Strictly convex domain; Space form
Citation
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, v.61, no.3, pp.621 - 639
Journal Title
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY
Volume
61
Number
3
Start Page
621
End Page
639
URI
https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/145852
DOI
10.1007/s10455-022-09828-2
ISSN
0232-704X
Abstract
Let C be a strictly convex domain in a three-dimensional Riemannian manifold with sectional curvature bounded above by a constant, and let Sigma be a constant mean curvature surface with free boundary in C. We provide a pinching condition on the length of the traceless second fundamental form on Sigma which guarantees that the surface is homeomorphic to either a disk or an annulus. Furthermore, under the same pinching condition, we prove that if C is a geodesic ball of three-dimensional space forms, then Sigma is either a spherical cap or a Delaunay surface.
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