发表机构
School of Mathematics and Statistics, Xinyang Normal University（信阳师范大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究空间形式中规范化Hessian和方程及其商方程的过定问题，证明在星形或Dirichlet值上界条件下区域为测地球，并推广至无星形假设情形，方法为辅助函数与Rellich–Pohožaev恒等式。
AI 中文摘要
我们研究空间形式中规范化Hessian和方程及其商方程的过定问题。方程和边界条件蕴含可容许性和椭圆性。对于商方程，我们证明若区域严格星形，或Dirichlet值满足上界，则区域为测地球。我们还证明了无星形假设下Hessian和方程的相应结果。证明使用两个辅助函数和Rellich–Pohožaev恒等式。
英文摘要
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.
