Abstract. In this paper we present some new ideas to derive a priori second order estiamtes for a wide class of fully nonlinear parabolic equations. Our methods, which produce new existence results for the initial-boundary value problems in R n , are powerful enough to work in general Riemannian manifolds.Mathematical Subject Classification (2010): 35K10, 35K55, 58J35, 35B45.

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We prove the existence of a complete locally Lipschitz continuous hypersurface in weak sense with prescribed Weingarten curvature and asymptotic boundary at infinity in hyperbolic space under certain assumptions.

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