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arXiv · 2304.07614

An eigenvalue problem for prescribed curvature equations

Taehun Lee
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Abstract

We study an eigenvalue problem for prescribed $\sigma_k$-curvature equations of star-shaped, $k$-convex, closed hypersurfaces. We establish the existence of a unique eigenvalue and its associated hypersurface, which is also unique, provided that the given data is even. Moreover, we show that the hypersurface must be strictly convex. A crucial aspect of our proof involves deriving uniform estimates in $p$ for $L_p$-type prescribed curvature equations.

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Taehun Lee. 2023-04-15. An eigenvalue problem for prescribed curvature equations. https://arxiv.org/abs/2304.07614

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