PreprintCC BY-NC-SA 4.0arXiv
Regularization and Hölder continuity for complex Hessian equations on Hermitian manifolds
Abstract
Let (M,ω) be a compact Hermitian manifold, and let Γ be a symmetric convex cone. We develop a quantitative regularization method for Γ-admissible functions. As an application, we prove Hölder continuity for every pluripotential solution of complex m-Hessian equations whose right-hand sides belong to Lp, for p>n/m. These results extend to a more general class of complex Hessian equations satisfying the structural condition used by Guo--Phong--Tong.
Related
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BibTeX
@misc{xu2026regularization,
title = {{Regularization and Hölder continuity for complex Hessian equations on Hermitian manifolds}},
author = {Yulun Xu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.15552},
eprint = {2608.15552},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.15552},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Regularization and Hölder continuity for complex Hessian equations on Hermitian manifolds
AU - Yulun Xu
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2608.15552
UR - https://arxiv.org/abs/2608.15552
AB - Let (M,ω) be a compact Hermitian manifold, and let Γ be a symmetric convex cone. We develop a quantitative regularization method for Γ-admissible functions. As an application, we prove Hölder continuity for every pluripotential solution of complex m-Hessian equations whose right-hand sides belong to L^p, for p>n/m. These results extend to a more general class of complex Hessian equations satisfying the structural condition used by Guo--Phong--Tong.
ER -