Contents
Prologue
Split-type Canonical Metrics and Related Geometric PDEs Hao Fang and Joshua Jordan 1
The Generalized Kahler Calabi-Yau Problem Xin Fu 13
Advances in the Volume Conjectures Huabin Ge and Chuwen Wang 26
Recent Progress on Austere Submanifolds Jianquan Ge and Yi Zhou 42
Multi-marginal Optimal Transport on Metric Measure Spaces Bangxian Han, Dengyu Liu, Zhuonan Zhu 56
Foliation of Area Minimizing Hypersurfaces in Asymptotically Flat Manifolds and Schoen’s Conjecture SHIHANG He, YUGUANG SHI, HAOBIN Yu 74
Classification and Uniqueness of Solutions to the Isotropic Lp Dual Minkowski Problem Haizhong Li and Yao Wan 86
Index and Total Curvature of Minimal Surfaces in Nonpositively Curved Symmetric Spaces QlONGLlNG Li 112
Recent Results on Complete Kahler Manifolds with Nonnegative Ricci Curvature Gang Liu 124
A Survey of Counterexamples to Regularity and Bernstein Property for Complex Monge-Ampere Equations ——JlAXIANG WANG AND WENLONG WANG 137
Kahler-Ricci Solitons and Optimal Degenerations of Fano Manifolds Linsheng Wang 152
The Partial Legendre Transform in Monge-Ampere Equations Ling Wang and Bin Zhou 161
On the Structure of Compact Kahler Manifolds with Nonnegative Holomorphic Sectional Curvature SHIYU ZHANG 178
Examples Related to Ricci Limit Spaces and Topology Shengxuan Zhou 186
The Existence Problem for Noncompact Completed Convex Sets in a Cone Baocheng Zhu 195
Calabi-Yau Type Theorem for Manifolds with Nonnegative Scalar Curvature Jintian Zhu 211