Prologue

Chapters in this book

1. Frontmatter i
2. Prologue iii
3. Contents v
4. Critical Allard Regularity in Dimension Two and Its Application 1
5. A Survey on the Complex Hessian Equation on Compact Kähler Manifolds 14
6. Minimal Graphs over Manifolds 28
7. Deformation Quantization and Noncommutative Differential Geometry 48
8. The Isoperimetric Problem in Riemannian Manifolds Endowed with Conformal Vector Fields 69
9. Adiabatic Limit Formula for Bismut-Cheeger Eta Forms 81
10. Optimal Degeneration Problem of Fano Threefolds 95
11. Spaces with Ricci Curvature Lower Bounds 103
12. Harmonic Metrics and Higgs Bundles 120
13. Pluriclosed Flow on Hermitian-Symplectic Manifolds 134
14. Weyl’s Lemma on RCD(K,N)-spaces and an Application to PDEs on Rⁿ 140
15. Quadratic Hessian Equation 157
16. Transcendental Okounkov Bodies 178
17. Log Gradient Estimates for Heat Type Equations on Manifolds 186