An eigenvalue problem for prescribed curvature equations

2023/04/15 by Lee, Taehun · 1 citation
#53C42 (Primary) 35J60 35P30 (Secondary) #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.07614

Abstract

We study an eigenvalue problem for prescribed σ_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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