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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