Surveys in Geometric Analysis – Volume 2, 2018, livre ebook

Geometric analysis has been a very important and active research field at the frontier of mathematics for last few decades, and many important achievements have been made in this field. The development of geometric analysis has played a key role in establishing numerous basic theories and solving long-standing problems in mathematics. It is a field worthy of much continued exploration.

Since the late 1990s, Peking University has taken the lead in organizing the annual Workshop on Geometric Analysis with participation of universities and research institutions from China and abroad. This work refers to the 2018 edition of the Workshop and is the second volume of a dedicated book series that aims to present the progress of Chinese and global research in geometric analysis by curating a selection of high-quality papers submitted by scholars to the annual Workshop on Geometric Analysis. It provides readers with a comprehensive overview of the latest trends, methods, and breakthroughs in the field, and serves as a valuable resource for ongoing research.

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

E-Regularity of Harmonie-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 Compactification of Lie Groups .............YAN LI and BIN ZHOU 64

Clifford Algebra, Isoparametric Foliation and Related Geometric Constructions ..CHAO QIAN and ZIZHOU TANG 83

The Kahler-Ricci Flow with Cusp Singularities on Projective Manifolds......... LIANG MING SHEN 98

On the Rigidity and Gap Theorem for Liouville's Equation....WEIMING SHEN 108

Existence of Conie 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

Sorne Recent Results on Nirenberg Problem ..................JINGANG XIONG 167