Contents Prologue Fundamental Gap Comparison Xianzhe Dai， Shoo Seto and Guofang Wei 1 Combinatorial Ricci Flows with Applications to 3-dimensional Geometry and Topology Huabin Ge 17 ε-Regularity of Harmonic-Einstein Equations Huabin Ge and Wenshuai Jiang 37 Free Boundary Minimal Hypersurfaces with Least Area Qiang Guang， Zhichao Wang and Xin Zhou 45 Babuska Problem in Composite Material Haigang Li 51 Energy Functionals and Canonical Metrics on Polarized Compacti-cation of Lie Groups Yan Li and Bin Zhou 64 Cliord Algebra， Isoparametric Foliation and Related Geometric Constructions Chao Qian and Zizhou Tang 83 The Kahler-Ricci Flow with Cusp Singularities on Projective Manifolds Liangming Shen 98 On the Rigidity and Gap Theorem for Liouville's Equation Weiming Shen 108 Existence of Conic Kahler-Einstein Metrics and Log K-Polystable Feng Wang 121 Rigidity of Free Boundary CMC Hypersurfaces in a Ball Guofang Wang and Chao Xia 138 Rigidity of Entire Self-Shrinking Solutions to Kahler-Ricci Flow: An Overview Wenlong Wang 154 Some Recent Results on Nirenberg Problem Jingang Xiong 167
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