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