论文标题
几何分析中的辅助蒙格 - 安培方程
Auxiliary Monge-Ampere equations in geometric analysis
论文作者
论文摘要
这是对特定类别的辅助复合物蒙格 - 安培方程的介绍，该方程在$ l^\ infty $估计中对完全非线性方程式和复杂几何形状中的各种问题发挥了作用。审查了基本的比较不平等现象，并显示在许多情况下适用。 Adapted to symplectic geometry, with the auxiliary equation given now by a real Monge-Ampère equation, the method gives an improvement of an earlier theorem of Tosatti-Weinkove-Yau, reducing Donaldson's conjecture on the Calabi-Yau equation with a taming symplectic form from an exponential bound to an $L^1$ bound.
This is an introduction to a particular class of auxiliary complex Monge-Ampère equations which had been instrumental in $L^\infty$ estimates for fully non-linear equations and various questions in complex geometry. The essential comparison inequalities are reviewed and shown to apply in many contexts. Adapted to symplectic geometry, with the auxiliary equation given now by a real Monge-Ampère equation, the method gives an improvement of an earlier theorem of Tosatti-Weinkove-Yau, reducing Donaldson's conjecture on the Calabi-Yau equation with a taming symplectic form from an exponential bound to an $L^1$ bound.
