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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

Qinian Jin 1, and  YanYan Li 2,

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

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