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Rigidity for Convex Entire Solutions to the k-Hessian Equation
Abstract
We prove that for each 3≤ k≤ n−1 a convex C2 entire solution of σk equation in ℝn with positive constant right hand side is a quadratic polynomial, without a growth assumption on the solution itself.
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BibTeX
@misc{zhou2026rigidity,
title = {{Rigidity for Convex Entire Solutions to the $k$-Hessian Equation}},
author = {Xingchen Zhou and Ruixuan Zhu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20445},
eprint = {2609.20445},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20445},
}
RIS
TY - UNPB
TI - Rigidity for Convex Entire Solutions to the k-Hessian Equation
AU - Xingchen Zhou
AU - Ruixuan Zhu
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20445
UR - https://arxiv.org/abs/2609.20445
AB - We prove that for each 3≤ k≤ n−1 a convex C^2 entire solution of σ_k equation in ℝ^n with positive constant right hand side is a quadratic polynomial, without a growth assumption on the solution itself.
ER -