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Hessian Estimates for Convex Solutions of Hessian Quotient Equations via Compactness
Abstract
We give a compactness proof of interior Hessian estimates for convex solutions of σn(D2u)/σn−2(D2u)=1 and σn(D2u)/σn−1(D2u)=f(x,u,Du)>0, with 1/f concave in the gradient variable in the latter case, revisiting results of Lu and Fung.
Related
- Interior Hessian estimates for k-convex solutions of Hessian quotient equations with 2k>n
- Interior Hessian estimates for k-convex solutions of Hessian quotient equations
- Interior estimates for Hessian quotient equations
- Poincaré-Type Hessian Quotient Equations
- A class of sum Hessian quotient equations arising in conformal geometry
BibTeX
@misc{liu2026hessian,
title = {{Hessian Estimates for Convex Solutions of Hessian Quotient Equations via Compactness}},
author = {Jianxiang Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08442},
eprint = {2610.08442},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08442},
}
RIS
TY - UNPB
TI - Hessian Estimates for Convex Solutions of Hessian Quotient Equations via Compactness
AU - Jianxiang Liu
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.08442
UR - https://arxiv.org/abs/2610.08442
AB - We give a compactness proof of interior Hessian estimates for convex solutions of σ_n(D^2u)/σ_n−2(D^2u)=1 and σ_n(D^2u)/σ_n−1(D^2u)=f(x,u,Du)>0, with 1/f concave in the gradient variable in the latter case, revisiting results of Lu and Fung.
ER -