PreprintCC BY 4.0arXiv
Overdetermined problems for sum Hessian equations in the space forms
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.
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BibTeX
@misc{cheng2026overdetermined,
title = {{Overdetermined problems for sum Hessian equations in the space forms}},
author = {Cheng Cheng and Yingbo Han},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05631},
eprint = {2610.05631},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05631},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Overdetermined problems for sum Hessian equations in the space forms
AU - Cheng Cheng
AU - Yingbo Han
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05631
UR - https://arxiv.org/abs/2610.05631
AB - 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.
ER -