Starshaped compact hypersurfaces with prescribed k-th mean curvature in hyperbolic space

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May 2006, 15(2): 367-377. doi: 10.3934/dcds.2006.15.367

Starshaped compact hypersurfaces with prescribed $k$-th mean curvature in hyperbolic space

1.	Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854, United States
2.	Department of Mathematics, Rutgers University, Hill Center, 110 Frelinghuysen Rd., Piscataway, NJ 08854

Received April 2005 Revised December 2005 Published March 2006

Abstract
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In this paper we consider the problem of finding a star-shaped compact hypersurface with prescribed $k$-th mean curvature in hyperbolic space. Under some sufficient conditions, we obtain an existence result by establishing a priori estimates and using degree theory arguments.

Keywords: a priori estimates., Hyperbolic space, k-th mean curvature.

Mathematics Subject Classification: Primary: 53C42; Secondary: 35J6.

Citation: Qinian Jin, YanYan Li. Starshaped compact hypersurfaces with prescribed $k$-th mean curvature in hyperbolic space. Discrete & Continuous Dynamical Systems - A, 2006, 15 (2) : 367-377. doi: 10.3934/dcds.2006.15.367

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