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Uniqueness of the Catenoid and the Delaunay Surface via a One-Parameter Family of Touching Spheres
- Min, Sung-Hong;
- Seo, Keomkyo
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0초록
We provide a new characterization of the catenoid and the Delaunay surface among constant mean curvature surfaces touching a one-parameter family of spheres along arcs in a 3-dimensional Euclidean space. Furthermore we prove a higher-dimensional analogue for constant mean curvature hypersurfaces. We also give a generalization of the classical theorem due to Joachimsthal. © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
키워드
Catenoid; constant mean curvature; Delaunay surface; minimal surface; touching sphere; BOUNDARY MINIMAL-SURFACES; INDEX CHARACTERIZATION; GAP THEOREM; HYPERSURFACES; TORI
- 제목
- Uniqueness of the Catenoid and the Delaunay Surface via a One-Parameter Family of Touching Spheres
- 저자
- Min, Sung-Hong; Seo, Keomkyo
- 발행일
- 2023-04
- 유형
- Article
- 권
- 78
- 호
- 2