发表机构
Rutgers University（罗格斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对紧致厄米流形上的凹完全非线性椭圆方程，提出一种不依赖Hou-Ma-Wu估计和Liouville定理的梯度估计直接证明方法，并结合稳定性估计与比较论证，同时给出紧致Kähler流形上复Hessian估计的独立证明。
AI 中文摘要
复Hessian方程的梯度估计的已知证明依赖于Hou-Ma-Wu的二阶估计以及Dinew-Kolodziej的Liouville定理。本文中，我们给出了紧致厄米流形上凹完全非线性椭圆方程的梯度估计的直接证明，该证明既不使用Hou-Ma-Wu估计，也不使用Liouville定理。相反，该证明将稳定性估计与对邻近光滑容许函数的比较论证相结合。我们还基于Dirichlet格林函数，在算子的附加假设下，给出了紧致Kähler流形上复Hessian估计的独立证明。
英文摘要
The known proofs of the gradient estimate for complex Hessian equations rely on the second order estimate of Hou-Ma-Wu and on a Liouville theorem of Dinew-Kolodziej. In this paper, we give a direct proof of the gradient estimate for concave fully nonlinear elliptic equations on compact Hermitian manifolds, which uses neither the Hou-Ma-Wu estimate nor the Liouville theorem. Instead, the proof combines a stability estimate with a comparison argument against nearby smooth admissible functions. We also give an independent proof of the complex Hessian estimate on compact Kähler manifolds, based on Dirichlet Green's functions, under additional assumptions on the operator.
