Year: 2026
Type: preprint
Abstract: We study overdetermined problems for normalized sum Hessian equations and their quotients in the space forms. The equations and boundary conditions imply admissibility and ellipticity. For quotient equations, we prove that the domain is a geodesic ball if it is strictly star-shaped, or if the Dirichlet value satisfies an upper bound. We also prove the corresponding result for sum Hessian equations without star-shapedness. The proofs use two auxiliary functions and a Rellich--Pohožaev identity.
Source: arXiv (Cornell University)
Authors: Cheng, Cheng, Han, Yingbo
Institution: Xinyang Normal University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G4199253425
OpenAlex ID: W7220744167