Contents
Prologue
Recent Progress on the Formation of Trapped Surfaces and Black Holes Junbin Li 1
Notes on Weighted K.hler-Ricci Solitons Chi Li 18
A Monge-Ampère Type Functional and Related Prescribing Curvature Problems Qi-Rui Li 62
The Obata Type Integral Identity and Its Application Daowen Lin; Xi-Nan Ma; Qianzhong Ou 81
A Brief Survey on a Recent Generalization of Cohn-Vossen Inequality on Certain K.hler Manifolds Gang Liu 111
A Brief Summary of the Recent Global Regularity for Monge-Ampère Equations Jiakun Liu 121
Isoparametric Submanifolds and Mean Curvature Flow Xiaobo Liu 145
Isolated Singularities of the Yamabe Equation with Non-flat Metrics Jingang Xiong 181
The Optimal Exponent of Certain Moser-Trudinger Type Inequalities on Projective Manifolds Kewei Zhang 189
Lower Bound of Modified K-energy on a Fano Manifold with Degeneration for K.hler-Ricci Solitons Liang Zhang 210
Some Regularity Estimates of the Complex Monge-Ampère Equation Xi Zhang 220
Topology of Surfaces with Finite Willmore Energy Jie Zhou 235
Finite Generation and the K.hler-Ricci Soliton Degeneration Ziquan Zhuang 245
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