Hölder continuity of solutions to the complex Monge-Ampère equation with the right hand side in L^p. The case of compact Kähler manifolds

紧 Kähler 流形自同构的所有阶指数混合与 CLT

Exponential mixing of all orders and CLT for automorphisms of compact K{ä}hler manifolds

本文研究上同调作用简单的紧 Kähler 流形自同构，证明其唯一最大熵测度对 Hölder 可观测量具有所有阶指数混合性，并推出 CLT，结果覆盖所有正熵紧 Kähler 曲面自同构。

Stability of solutions to complex Monge-Ampere flows

We establish a stability result for elliptic and parabolic complex Monge-Amp{è}re equations on compact K{ä}hler manifolds, which applies in particular to the K{ä}hler-Ricci flow. Dedicated to Jean-Pierre Demailly on the occasion of his 60th birthday.

Pluripotential Monge-Amp{è}re flows in Big Cohomology Classes

We study pluripotential complex Monge-Ampère flows in big cohomology classes on compact K{ä}hler manifolds. We use the Perron method, considering pluripotential subsolutions to the Cauchy problem. We prove that, under natural assumptions on the data, the upper envelope of all subsolutions is continuous in space and semi-concave in time, and provides a unique pluripotential solution with such regularity. We apply this theory to study pluripotential K{ä}hler-Ricci flows on compact K{ä}hler manifolds of general type as well as on stable varieties.

Continuity of Monge-Amp{è}re Potentials in Big Cohomology Classes

Extending DiNezza-Lu's approach to the setting of big cohomology classes, we prove that solutions of degenerate complex Monge-Amp{è}re equations on compact K{ä}hler manifolds are continuous on a Zariski open set. This allows us to show that singular K{ä}hler-Einstein metrics on log canonical varieties of general type have continuous potentials on the ample locus outside of the non-klt part.

Regularity of push-forward of Monge-Amp{è}re measures

We prove that the image under any dominant meromorphic map of the Monge-Amp{è}re measure of a H{ö}lder continuous quasi-psh function still possesses a H{ö}lder potential. We also discuss the case of lower regularity.

Hermitian流形上的复Monge-Ampère方程：从有界解到光滑解

Complex Monge-Amp{è}re equations on Hermitian Manifolds: From bounded to smooth solutions

研究紧致Hermitian流形上复Monge-Ampère方程有界弱解的正则性，通过支配原理和先验估计证明有界解在数据正则点集光滑，并恢复已有结果。