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

Qinian Jin; YanYan Li

doi:10.3934/dcds.2006.15.367

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2006, Volume 15, Issue 2: 367-377. Doi: 10.3934/dcds.2006.15.367

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

Received: March 31, 2005

Revised: November 30, 2005

Published: March 2006

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Abstract

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.

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Mathematics Subject Classification: Primary: 53C42; Secondary: 35J60.

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