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C1,1 Regularity Global Estimates for Homogeneous Complex Hessian Equations on Punctured Domains
Abstract
In this paper, we prove the C1,1 regularity of Green functions associated with the complex k-Hessian operator for 1≤ k<n, and give a new proof of the corresponding regularity of pluricomplex Green functions. We establish real Hessian estimates for approximating problems associated with homogeneous complex Hessian equations on punctured domains. The main idea is to introduce new auxiliary functions generated by complex linear vector fields to reduce the global real Hessian estimate to the boundary. We also treat the complex Monge-Ampère case. Similar real Hessian estimates also works for the exterior problem.
Related
- On the Local Regularity of Homogeneous Complex Monge-Ampère Equations
- Regularity Estimates for Quasilinear Elliptic Equations with Measure Data and Matrix-Valued Weight
- Potential estimates and improved Sobolev regularity for nonlocal fully nonlinear elliptic equations
- Concavity-Free L∞ Estimates and Stability for Fully Nonlinear Complex Equations
- Geometric Holder estimates for complex Monge-Ampere equations
BibTeX
@misc{gao2026regularity,
title = {{$C^1,1$ Regularity Global Estimates for Homogeneous Complex Hessian Equations on Punctured Domains}},
author = {Zhenghuan Gao and Xi-Nan Ma and Bao Yu and Dekai Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14692},
eprint = {2609.14692},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14692},
}
RIS
TY - UNPB
TI - C^1,1 Regularity Global Estimates for Homogeneous Complex Hessian Equations on Punctured Domains
AU - Zhenghuan Gao
AU - Xi-Nan Ma
AU - Bao Yu
AU - Dekai Zhang
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14692
UR - https://arxiv.org/abs/2609.14692
AB - In this paper, we prove the C^1,1 regularity of Green functions associated with the complex k-Hessian operator for 1≤ k<n, and give a new proof of the corresponding regularity of pluricomplex Green functions. We establish real Hessian estimates for approximating problems associated with homogeneous complex Hessian equations on punctured domains. The main idea is to introduce new auxiliary functions generated by complex linear vector fields to reduce the global real Hessian estimate to the boundary. We also treat the complex Monge-Ampère case. Similar real Hessian estimates also works for the exterior problem.
ER -