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Geometric Analysis

In Honor of Gang Tian's 60th Birthday

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  • © 2020

Overview

Editors:
  1. Jingyi Chen

    1. Department of Mathematics, The University of British Columbia, Vancouver, Canada

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  2. Peng Lu

    1. Department of Mathematics, University of Oregon, Eugene, USA

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  3. Zhiqin Lu

    1. Department of Mathematics, University of California, Irvine, Irvine, USA

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  4. Zhou Zhang

    1. School of Mathematics and Statistics, University of Sydney, Sydney, Australia

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  • Presents information on recent cutting edge progress in the field
  • Offers starters in the topic an introduction and paramount view of the subfields
  • Contributions from leading experts

Part of the book series: Progress in Mathematics (PM, volume 333)

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Table of contents (24 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Big and Nef Classes, Futaki Invariant and Resolutions of Cubic Threefolds

    • Claudio Arezzo, Alberto Della Vedova
    Pages 1-16

  3. Bottom of Spectra and Amenability of Coverings

    • Werner Ballmann, Henrik Matthiesen, Panagiotis Polymerakis
    Pages 17-35

  4. Some Remarks on the Geometry of a Class of Locally Conformally Flat Metrics

    • Sun-Yung A. Chang, Zheng-Chao Han, Paul Yang
    Pages 37-56

  5. Analytical Properties for Degenerate Equations

    • Tobias Holck Colding, William P. Minicozzi II
    Pages 57-70

  6. Equivariant K-theory and Resolution I: Abelian Actions

    • Panagiotis Dimakis, Richard Melrose
    Pages 71-92

  7. On the Existence Problem of Einstein–Maxwell Kähler Metrics

    • Akito Futaki, Hajime Ono
    Pages 93-111

  8. Local Moduli of Scalar-flat Kähler ALE Surfaces

    • Jiyuan Han, Jeff A. Viaclovsky
    Pages 113-135

  9. Singular Ricci Flows II

    • Bruce Kleiner, John Lott
    Pages 137-155

  10. An Inequality Between Complex Hessian Measures of Hölder Continuous m-subharmonic Functions and Capacity

    • Sławomir Kołodziej, Ngoc Cuong Nguyen
    Pages 157-166

  11. A Guided Tour to Normalized Volume

    • Chi Li, Yuchen Liu, Chenyang Xu
    Pages 167-219

  12. Towards a Liouville Theorem for Continuous Viscosity Solutions to Fully Nonlinear Elliptic Equations in Conformal Geometry

    • YanYan Li, Luc Nguyen, Bo Wang
    Pages 221-244

  13. Arsove–Huber Theorem in Higher Dimensions

    • Shiguang Ma, Jie Qing
    Pages 245-263

  14. From Local Index Theory to Bergman Kernel: A Heat Kernel Approach

    • Xiaonan Ma
    Pages 265-286

  15. Fourier–Mukai Transforms, Euler–Green Currents, and K-Stability

    • Sean Timothy Paul, Kyriakos Sergiou
    Pages 287-303

  16. The Variations of Yang–Mills Lagrangian

    • Tristan Rivière
    Pages 305-379

  17. Tian’s Properness Conjectures:An Introduction to Kähler Geometry

    • Yanir A. Rubinstein
    Pages 381-443

  18. Ancient Solutions in Geometric Flows

    • Natasa Sesum
    Pages 445-463

  19. The Kähler–Ricci Flow on CP2

    • Jian Song
    Pages 465-469

  20. Pluriclosed Flow and the Geometrization of Complex Surfaces

    • Jeffrey Streets
    Pages 471-510
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Keywords

About this book

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, Sławomir Kołodziej, 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.

Editors and Affiliations

  • Department of Mathematics, The University of British Columbia, Vancouver, Canada

    Jingyi Chen

  • Department of Mathematics, University of Oregon, Eugene, USA

    Peng Lu

  • Department of Mathematics, University of California, Irvine, Irvine, USA

    Zhiqin Lu

  • School of Mathematics and Statistics, University of Sydney, Sydney, Australia

    Zhou Zhang

Bibliographic Information

  • Book Title: Geometric Analysis

  • Book Subtitle: In Honor of Gang Tian's 60th Birthday

  • Editors: Jingyi Chen, Peng Lu, Zhiqin Lu, Zhou Zhang

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-34953-0

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2020

  • Hardcover ISBN: 978-3-030-34952-3Published: 11 April 2020

  • Softcover ISBN: 978-3-030-34955-4Published: 11 April 2021

  • eBook ISBN: 978-3-030-34953-0Published: 10 April 2020

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: X, 616

  • Number of Illustrations: 17 b/w illustrations, 8 illustrations in colour

  • Topics: Global Analysis and Analysis on Manifolds

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