# Hypersurfaces of prescribed curvature in hyperbolic space [electronic resource] /

Abstract (Summary)

In this paper we consider the problem of existence of hypersurfaces with prescribed curvature in hyperbolic space. We use the upper half-space model of hyperbolic space. The hypersurfaces we consider are given as graphs of positive functions on some domain [omega belongs to (real set)superscript n] satisfying equations of form f(A) = f([kappa?, . . . ,kappa superscript n]) = [psi] , where A is the second fundamental form of a hypersurface, f(A) is a smooth symmetric function of the eigenvalues of A and [psi] is a function of position. If we impose certain conditions on f and [psi], the above equation can be treated as an elliptic, fully non-linear partial differential equation G(D²u,Du, u) = [psi], (x, u). We then derive an existence result for the corresponding Dirichlet problem.
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School:The University of Tennessee at Chattanooga

School Location:USA - Tennessee

Source Type:Master's Thesis

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