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 ��-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