Abstract

PERDOMO, OSCAR. Embedded CMC Hypersurfaces on Hyperbolic Spaces. Rev.colomb.mat. [online]. 2011, vol.45, n.1, pp.81-96. ISSN 0034-7426.

In this paper we will prove that for every integer n>1, there exists a real number H₀<-1 such that every H∈ (-∞,H₀) can be realized as the mean curvature of an embedding of H^n-1\times S¹ in the n+1-dimensional space Hⁿ⁺¹. For n=2 we explicitly compute the value H₀. For a general value n, we provide a function ξ_n defined on (-∞,-1), which is easy to compute numerically, such that, if ξ_n(H)>-2π, then, H can be realized as the mean curvature of an embedding of H^n-1\times S¹ in the (n+1)-dimensional space Hⁿ⁺¹.

Keywords : Principal curvatures; Hyperbolic spaces; Constant mean curvature; CMC; Embeddings.

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