PreprintCC BY 4.0arXiv
A Comparison Pogorelov Estimate for Graphical σk-Curvature Equations
Abstract
We establish comparison Pogorelov estimates for admissible solutions of graphical σk-curvature equations, extending the two-surface estimate of Qiu and Yan for the graphical scalar curvature equation. The comparison graph is assumed only to be k-admissible, with a bounded slope and a positive interior gap that vanishes on the boundary. The estimates cover 2≤ k<n for prescribed data f(x,u), and n/2≤ k<n for general data $f(x,u,Du)$. The proof combines the two-surface localization and mixed Gårding comparison of Qiu and Yan with Yan's spectral concavity inequality and an angle-function weight.
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BibTeX
@misc{zhou2026comparison,
title = {{A Comparison Pogorelov Estimate for Graphical $σ_k$-Curvature Equations}},
author = {Jundong Zhou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03062},
eprint = {2610.03062},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03062},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Comparison Pogorelov Estimate for Graphical σ_k-Curvature Equations
AU - Jundong Zhou
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03062
UR - https://arxiv.org/abs/2610.03062
AB - We establish comparison Pogorelov estimates for admissible solutions of graphical σ_k-curvature equations, extending the two-surface estimate of Qiu and Yan for the graphical scalar curvature equation. The comparison graph is assumed only to be k-admissible, with a bounded slope and a positive interior gap that vanishes on the boundary. The estimates cover 2≤ k<n for prescribed data f(x,u), and n/2≤ k<n for general data $f(x,u,Du)$. The proof combines the two-surface localization and mixed Gårding comparison of Qiu and Yan with Yan's spectral concavity inequality and an angle-function weight.
ER -