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- Title
An Eigenvalue Problem for Prescribed Curvature Equations.
- Authors
Lee, Taehun
- 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.
- Subjects
EIGENVALUES; CURVATURE; EQUATIONS; HYPERSURFACES
- Publication
IMRN: International Mathematics Research Notices, 2024, Vol 2024, Issue 10, p8296
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnad220