本书内容是几何分析领域优秀的科研工作者所写的综述性报告，文章汇报了几何分析领域的前沿热点。包括包括:紧Kahler流形上复hessian方程的研究、偏微分方程和黎曼几何、不变体系、几何可变体系、瞬变体系和刚片、自由度与辛几何、代数几何和物理中的超弦理论、二维非线性偏微分方程、Ricci流、Gromov-Witten不变量理论、Kaehler-Ricci流，Kaehler-Ricci孤立子专享性，调和映射紧性，高余维平均曲率流等。

Contents
Critical Allard Regularity in Dimension Two and Its Application  Yuchen Bi, Jie Zhou 1
A Survey on the Complex Hessian Equation on Compact K.hler Manifolds  Jianchun Chu 14
Minimal Graphs over Manifolds  Qi Ding 28
Deformation Quantization and Noncommutative Differential Geometry  Haoyuan Gao, Xiao Zhang 48
The Isoperimetric Problem in Riemannian Manifolds Endowed with Conformal Vector Fields  Jiayu Li, Shujing Pan 69
Adiabatic Limit Formula for Bismut-Cheeger eta Forms  Bo Liu, Mengqing Zhan 81
Optimal Degeneration Problem of Fano Threefolds  Minghao Miao 95
Spaces with Ricci Curvature Lower Bounds  Jiayin Pan, Guofang Wei 103
Harmonic Metrics and Higgs Bundles  Di Wu 120
Pluriclosed Flow on Hermitian-Symplectic Manifolds  Yanan Ye 134
Weyl’s Lemma on RCD(K,N)-spaces and an Application to PDEs on Rn  Peng Yu, Hui-Chun Zhang, Xi-Ping Zhu 140
Quadratic Hessian Equation  Yu Yuan 157
Transcendental Okounkov Bodies  Kewei Zhang 178
Log Gradient Estimates for Heat Type Equations on Manifolds  Qi S. Zhang 186