Free boundary constant mean curvature surfaces in a strictly convex three-manifold
- Authors
- Min, Sung-Hong; Seo, 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
- Pages
- 19
- 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
1572-9060
- 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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