Prescribed Weingarten curvature equations in warped product manifolds

Chenyang Liu; Jing Mao; Ya Gao

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arxiv 2111.01636 v2 pith:WF2UZ6MI submitted 2021-11-02 math.DG

Prescribed Weingarten curvature equations in warped product manifolds

Ya Gao , Chenyang Liu , Jing Mao This is my paper

classification math.DG

keywords curvatureproductwarpedweingartenequationsexistencemanifoldmanifolds

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In this paper, under suitable settings, we can obtain the existence of solutions to a class of prescribed Weingarten curvature equations in warped product manifolds of special type by the standard degree theory based on the a priori estimates for the solutions. This is to say that the existence of closed hypersurface (which is graphic with respect to the base manifold and whose $k$-th Weingarten curvature satisfies some constraint) in a given warped product manifold of special type can be assured.

Prescribed Weingarten curvature equations in warped product manifolds

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