PreprintarXiv licencearXiv
Alternative proof of the gradient estimate for complex Hessian equations
Abstract
For complex Hessian equations on compact Kähler manifolds, we give an alternative proof of the gradient estimate without using blow-up argument, and clarify its dependence on the right-hand side. In addition, using the similar approach, the case of Kähler manifolds with boundary is also investigated.
Related
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- Gradient Estimates for Hessian Equations with Measure Data
- Gradient potential estimates for k-Hessian equations
- On Polynomial Complex Hessian Equations I: Non-Linear Non-Spectral Elliptic Hessian Equations on Riemannian Manifolds
- Smoothness of bounded solutions to complex Hessian equations on compact Hermitian manifolds
BibTeX
@misc{chu2026alternative,
title = {{Alternative proof of the gradient estimate for complex Hessian equations}},
author = {Jianchun Chu and Yaxiong Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33091},
eprint = {2609.33091},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33091},
}
RIS
TY - UNPB
TI - Alternative proof of the gradient estimate for complex Hessian equations
AU - Jianchun Chu
AU - Yaxiong Liu
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33091
UR - https://arxiv.org/abs/2609.33091
AB - For complex Hessian equations on compact Kähler manifolds, we give an alternative proof of the gradient estimate without using blow-up argument, and clarify its dependence on the right-hand side. In addition, using the similar approach, the case of Kähler manifolds with boundary is also investigated.
ER -