Affiliation:
1. School of Mathematical Sciences , Xiamen University , 361005 Xiamen , P. R. China
Abstract
Abstract
In the first part of this paper, we consider a partially overdetermined mixed boundary value problem in space forms and generalize the main result in [11] to the case of general domains with partial umbilical boundary in space forms. Precisely, we prove that a partially overdetermined problem in a domain with partial umbilical boundary admits a solution if and only if the rest part of the boundary is also part of an umbilical hypersurface. In the second part of this paper, we prove a Heintze–Karcher–Ros-type inequality for embedded hypersurfaces with free boundary lying on a horosphere or an equidistant hypersurface in the hyperbolic space. As an application, we show an Alexandrov-type theorem for constant mean curvature hypersurfaces with free boundary in these settings.
Funder
National Natural Science Foundation of China
Subject
Applied Mathematics,Analysis
Reference30 articles.
1. M. S. Agranovich,
On a mixed Poincaré–Steklov type spectral problem in a Lipschitz domain,
Russ. J. Math. Phys. 13 (2006), no. 3, 239–244.
2. A. D. Aleksandrov,
Uniqueness theorems for surfaces in the large. V,
Vestnik Leningrad. Univ. 13 (1958), no. 19, 5–8.
3. N. Aronszajn,
A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order,
J. Math. Pures Appl. (9) 36 (1957), 235–249.
4. R. Bañuelos, T. Kulczycki, I. Polterovich and B. O. Siudeja,
Eigenvalue inequalities for mixed Steklov problems,
Operator Theory and its Applications,
Amer. Math. Soc. Transl. Ser. 2 231,
American Mathematical Society, Providence (2010), 19–34.
5. J. a. L. M. Barbosa and A. G. Colares,
Stability of hypersurfaces with constant r-mean curvature,
Ann. Global Anal. Geom. 15 (1997), no. 3, 277–297.
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