Prologue

Chapters in this book

1. Frontmatter i
2. Prologue iii
3. Contents v
4. Fundamental Gap Comparison 1
5. Combinatorial Ricci Flows with Applications to :!-dimensional Geometry and Topology 17
6. E-Regularity of Harmonic-Einstein Equations 37
7. Free Boundary Minimal Hypersurfaces with Least Area 45
8. Babuska Problem in Composite Material 51
9. Energy Functionals and Canonical Metrics on Polarized Compactification of Lie Groups 64
10. Clifford Algebra, Isoparametric Foliation and Related Geometric Constructions 83
11. The Kahler-Ricci Flow with Cusp Singularities on Projective Manifolds 98
12. On the Rigidity and Gap Theorem for Liouville's Equation 108
13. Existence of Conic Kahler-Einstein Metrics and Log K-Polystable 121
14. Rigidity of Free Boundary CMC Hypersurfaces in a Ball 138
15. Rigidity of Entire Self-Shrinking Solutions to Kahler-Ricci Flow: An Overview 154
16. Some Recent Results on Nirenberg Problem 167