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E-grāmata: Geometric Analysis: In Honor of Gang Tian's 60th Birthday

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  • Formāts: PDF+DRM
  • Sērija : Progress in Mathematics 333
  • Izdošanas datums: 10-Apr-2020
  • Izdevniecība: Springer Nature Switzerland AG
  • Valoda: eng
  • ISBN-13: 9783030349530
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  • Formāts: PDF+DRM
  • Sērija : Progress in Mathematics 333
  • Izdošanas datums: 10-Apr-2020
  • Izdevniecība: Springer Nature Switzerland AG
  • Valoda: eng
  • ISBN-13: 9783030349530
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This edited volume has a two-fold purpose. First, comprehensive survey articles provide a way for beginners to ease into the corresponding sub-fields. These are then supplemented by original works that give the more advanced readers a glimpse of the current research in geometric analysis and related PDEs.

The book is of significant interest for researchers, including advanced Ph.D. students, working in geometric analysis. Readers who have a secondary interest in geometric analysis will benefit from the survey articles.

The results included in this book will stimulate further advances in the subjects: geometric analysis, including complex differential geometry, symplectic geometry, PDEs with a geometric origin, and geometry related to topology.

Contributions by Claudio Arezzo, Alberto Della Vedova, Werner Ballmann, Henrik Matthiesen, Panagiotis Polymerakis, Sun-Yung A. Chang, Zheng-Chao Han, Paul Yang, Tobias Holck Colding, William P. Minicozzi II, Panagiotis Dimakis, Richard Melrose, Akito Futaki, Hajime Ono, Jiyuan Han, Jeff A. Viaclovsky, Bruce Kleiner, John Lott, Slawomir Kolodziej, Ngoc Cuong Nguyen, Chi Li, Yuchen Liu, Chenyang Xu, YanYan Li, Luc Nguyen, Bo Wang, Shiguang Ma, Jie Qing, Xiaonan Ma, Sean Timothy Paul, Kyriakos Sergiou, Tristan Rivière, Yanir A. Rubinstein, Natasa Sesum, Jian Song, Jeffrey Streets, Neil S. Trudinger, Yu Yuan, Weiping Zhang, Xiaohua Zhu and Aleksey Zinger.

Preface vii
A Brief Description of the Volume ix
Big and Nef Classes, Futaki Invariant and Resolutions of Cubic Threefolds
1(16)
C. Arezzo
A. Delia Vedova
Bottom of Spectra and Amenability of Coverings
17(20)
W. Ballmann
H. Matthiesen
P. Polymerakis
Some Remarks on the Geometry of a Class of Locally Conformally Flat Metrics
37(20)
S.-Y.A. Chang
Z.-C. Han
P. Yang
Analytical Properties for Degenerate Equations
57(14)
T.H. Colding
W.P. Minicozzi
Equivariant A"-theory and Resolution I: Abelian Actions
71(22)
P. Dimakis
R. Melrose
On the Existence Problem of Einstein-Maxwell Kahler Metrics
93(20)
A. Futaki
H. Ono
Local Moduli of Scalar-flat Kahler ALE Surfaces
113(24)
J. Han
J.A. Viaclovsky
Singular Ricci Flows II
137(20)
B. Kleiner
J. Lott
An Inequality Between Complex Hessian Measures of Holder Continuous m-subharmonic Functions and Capacity
157(10)
S. Kolodziej
N. C. Nguyen
A Guided Tour to Normalized Volume
167(54)
C. Li
Y. Liu
C. Xu
Towards a Liouville Theorem for Continuous Viscosity Solutions to Fully Nonlinear Elliptic Equations in Conformal Geometry
221(24)
Y. Li
L. Nguyen
B. Wang
Arsove-Huber Theorem in Higher Dimensions
245(20)
S. Ma
J. Qing
From Local Index Theory to Bergman Kernel: A Heat Kernel Approach
265(22)
X. Ma
Fourier-Mukai Transforms, Euler-Green Currents, and K-Stability
287(18)
S. T. Paul
K. Sergiou
The Variations of Yang-Mills Lagrangian
305(76)
T. Riviere
Tian's Properness Conjectures: An Introduction to Kahler Geometry
381(64)
Y.A. Rubinstein
Ancient Solutions in Geometric Flows
445(20)
N. Sesum
The Kahler-Ricci Flow on CP2
465(6)
J. Song
Pluriclosed Flow and the Geometrization of Complex Surfaces
471(40)
J. Streets
From Optimal Transportation to Conformal Geometry
511(10)
N.S. Trudinger
Special Lagrangian Equations
521(16)
Y. Yuan
Positive Scalar Curvature on Foliations: The Enlargeability
537(8)
W. Zhang
Kahler-Einstein Metrics on Toric Manifolds and G-manifolds
545(42)
X. Zhu
Some Questions in the Theory of Pseudoholomorphic Curves
587
A. Zinger