论文标题
复杂几何形状中的完全非线性退化椭圆方程
Fully non-linear degenerate elliptic equations in complex geometry
论文作者
论文摘要
我们为紧凑的赫尔米利亚歧管上的大型几何椭圆形方程的解决方案提供了一个先验的Hessian估计，该估计值与右侧函数的下限无关。这改善了székelyHidi的估计值，此外还适用于右侧退化的椭圆方程。作为一个应用程序，我们建立了最佳的$ c^{1,1} $ $（θ，m）$ - 在紧凑型Hermitian歧管上的subharmonic函数的定期性。
We derive an a priori real Hessian estimate for solutions of a large family of geometric fully non-linear elliptic equations on compact Hermitian manifolds, which is independent of a lower bound for the right-hand side function. This improves on the estimates of Székelyhidi and additionally applies to elliptic equations with a degenerate right-hand side. As an application, we establish the optimal $C^{1,1}$ regularity of envelopes of $(θ, m)$-subharmonic functions on compact Hermitian manifolds.
