Abstract
It is proved that an embedded hypersurface in a hemisphere of the Euclidean unit spherewith constant mean curvature and spherical boundary inherits, under certainconditions, the symmetries of its boundary. In particular, spherical caps are theonly such hypersurfaces whose boundary are geodesic spheres.
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References
Aleksandrov, A. D.: Uniqueness theorems for surfaces in the large V, Trans. Amer. Math. Soc. 21 (1962), 412-416.
Aleksandrov, A. D.: A characteristic property of spheres, Ann. Mat. Pura Appl. 58 (1962), 305-315.
Brito, F., Earp, R. S., Meeks, W. and Rosenberg, H.: Structure theorems for constant mean curvature surfaces bounded by a planar curve, Indiana Univ. Math. J. 40 (1991), 333-343.
Hsiang, W. Y.: On generalization of theorems of A. D. Aleksandrov and C. Delaunay on hypersurfaces of constant mean curvature, Duke Math. J. 49 (1982), 485-496.
Koiso, M.: Symmetry of hypersurfaces of constant mean curvature with symmetric boundary, Math. Z. 191 (1986), 567-574.
Kusner, R.: Global geometry of extremal surfaces in three-space. PhD Thesis, University of California, 1988.
Lira, J. H. S.: Existência e unicidade de hipersuperfícies com bordo e curvatura média constante em formas espaciais, PhD Thesis, Universidade Federal do Ceará, Brazil, 2000.
Nelli, B. and Rosenberg, H.: Some remarks on embedded hypersurfaces in hyperbolic space of constant mean curvature and spherical boundary, Ann. Global Anal. Geom. 13 (1995), 23-30.
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de Lira, J.H.S. Embedded Hypersurfaces in Sn+1 with Constant Mean Curvature and Spherical Boundary. Annals of Global Analysis and Geometry 21, 123–133 (2002). https://doi.org/10.1023/A:1014730524005
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DOI: https://doi.org/10.1023/A:1014730524005