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arXiv · 2111.01636

Prescribed Weingarten curvature equations in warped product manifolds

Ya Gao·Chenyang Liu·Jing Mao
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Abstract

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.

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Ya Gao, Chenyang Liu, Jing Mao. 2021-11-02. Prescribed Weingarten curvature equations in warped product manifolds. https://arxiv.org/abs/2111.01636

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