PreprintCC0arXiv
Interior Hessian estimates for k-convex solutions of Hessian quotient equations
Abstract
We study interior Hessian estimates for k-convex solutions of Hessian quotient equations σk(D2u)/σℓ(D2u)=1 with 2≤ k≤ n, 0 ≤ ℓ < k, and k−ℓ ∈{1,2}. We first adopt the unified quantitative separation-propagation method of Li--Wu [LW26b] to derive a doubling inequality, and then use the compactness argument of Shankar--Yuan [SY25] to obtain the estimates. This approach also applies to a class of general Hessian equations.
Related
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BibTeX
@misc{li2026interior,
title = {{Interior Hessian estimates for $k$-convex solutions of Hessian quotient equations}},
author = {Zhisu Li and Ke Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18252},
eprint = {2610.18252},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18252},
note = {CC0},
}
RIS
TY - UNPB
TI - Interior Hessian estimates for k-convex solutions of Hessian quotient equations
AU - Zhisu Li
AU - Ke Wu
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18252
UR - https://arxiv.org/abs/2610.18252
AB - We study interior Hessian estimates for k-convex solutions of Hessian quotient equations σ_k(D^2u)/σ_ℓ(D^2u)=1 with 2≤ k≤ n, 0 ≤ ℓ < k, and k−ℓ ∈{1,2}. We first adopt the unified quantitative separation-propagation method of Li--Wu [LW26b] to derive a doubling inequality, and then use the compactness argument of Shankar--Yuan [SY25] to obtain the estimates. This approach also applies to a class of general Hessian equations.
ER -