References & Citations
Mathematics > Analysis of PDEs
Title: $k$-convex hypersurfaces with prescribed Weingarten curvature in warped product manifolds
(Submitted on 6 May 2024 (v1), last revised 8 May 2024 (this version, v3))
Abstract: In this paper, we consider Weingarten curvature equations for $k$-convex hypersurfaces with $n<2k$ in a warped product manifold $\overline{M}=I\times_{\lambda}M$. Based on the conjecture proposed by Ren-Wang in \cite{Ren2}, which is valid for $k\geq n-2$, we derive curvature estimates for equation $\sigma_k(\kappa)= \psi (V, \nu (V))$ through a straightforward proof. Furthermore, we also obtain an existence result for the star-shaped compact hypersurface $\Sigma$ satisfying the above equation by the degree theory under some sufficient conditions.
Submission history
From: Xiaojuan Chen [view email][v1] Mon, 6 May 2024 12:18:41 GMT (15kb)
[v2] Tue, 7 May 2024 09:19:15 GMT (15kb)
[v3] Wed, 8 May 2024 12:59:09 GMT (15kb)
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