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Starshaped compact hypersurfaces with prescribed m-th mean curvature in elliptic space

By Qinian Jin and Yanyan Li


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. 1. Introduction. Let S n be the unit sphere in the Euclidean space R n+1, and let e be the standard metric on S n induced from R n+1. Suppose that (u, ρ) are the spherical coordinates in R n+1, where u ∈ S n, ρ ∈ [0, ∞). By choosing the smooth function ϕ(ρ): = sinh 2 ρ on [0, ∞) we can define a Riemannian metric h on the set {(u, ρ) : u ∈ S n, 0 ≤ ρ < ∞} as follow

Year: 2009
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