Skip to main content
SpringerLink
Log in
Book cover

Geometric Analysis of the Bergman Kernel and Metric

  • Textbook
  • © 2013

Overview

Authors:
  1. Steven G. Krantz

    1. Department of Mathematics, Washington University in St. Louis, St. Louis, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Several topics are presented for the first time in book form
  • Textbook for graduate students that will also benefit seasoned researchers in mathematics
  • Includes illustrative examples and carefully chosen exercises
  • Discusses applications to function theory, geometry, partial differential equations, and interpretations in terms of functional analysis
  • Includes supplementary material: sn.pub/extras

Part of the book series: Graduate Texts in Mathematics (GTM, volume 268)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 49.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 89.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (8 chapters)

  1. Front Matter

    Pages i-xiii
    Download chapter PDF

  2. Introductory Ideas

    • Steven G. Krantz
    Pages 1-69

  3. The Bergman Metric

    • Steven G. Krantz
    Pages 71-85

  4. Further Geometric and Analytic Theory

    • Steven G. Krantz
    Pages 87-116

  5. Partial Differential Equations

    • Steven G. Krantz
    Pages 117-145

  6. Further Geometric Explorations

    • Steven G. Krantz
    Pages 147-186

  7. Additional Analytic Topics

    • Steven G. Krantz
    Pages 187-250

  8. Curvature of the Bergman Metric

    • Steven G. Krantz
    Pages 251-271

  9. Concluding Remarks

    • Steven G. Krantz
    Pages 273-273

  10. Back Matter

    Pages 275-292
    Download chapter PDF
Back to top

Keywords

About this book

This text provides a masterful and systematic treatment of all the basic analytic and geometric aspects of Bergman's classic theory of the kernel and its invariance properties. These include calculation, invariance properties, boundary asymptotics, and asymptotic expansion of the Bergman kernel and metric. Moreover, it presents a unique compendium of results with applications to function theory, geometry, partial differential equations, and interpretations in the language of functional analysis, with emphasis on the several complex variables context. Several of these topics appear here for the first time in book form. Each chapter includes illustrative examples and a collection of exercises which will be of interest to both graduate students and experienced mathematicians.

Graduate students who have taken courses in complex variables
and have a basic background in real and functional analysis will find this textbook appealing. Applicable courses for either main or supplementary usage include those in complex variables, several complex variables, complex differential geometry, and partial differential equations. Researchers in complex analysis, harmonic analysis, PDEs, and complex differential geometry will also benefit from the thorough treatment of the many exciting aspects of Bergman's theory.

Reviews

From the book reviews:

“This book is a compendium on the current state of Bergman theory in several complex variables would be an excellent source for a graduate course on Bergman theory in several complex variables. It is a must have for graduate students in this area as well as mathematicians wanting to learn more about this theory. It begins with the basics and ends at the forefront of current research.” (Steven Deckelman, MAA Reviews, December, 2014)

“The monograph under review gives the reader a look at the ever-evolving Bergman theory. … The book covers a great deal of interesting topics on the Bergman kernel and metric. In particular, it abounds with useful and instructive calculation, much of which cannot be found elsewhere. It will certainly be an invaluable resource for students as well as seasoned researchers in geometric analysis of the Bergman kernel and metric.” (Jianbing Su, Mathematical Reviews, October, 2014)

Authors and Affiliations

  • Department of Mathematics, Washington University in St. Louis, St. Louis, USA

    Steven G. Krantz

About the author

Steven G. Krantz is one of Springer’s and Birkhäuser’s most prolific and popular authors in the field of functional analysis, geometric analysis, and partial differential equations. Krantz is the series editor of Birkhäuser’s ‘ Cornerstones’ graduate text series and the founder and editor-in-chief of “The Journal of Geometric Analysis”, considered a society journal previously published by the AMS and often acts as an advisor to several senior editors at Springer/ Birkhäuser . He is also editor-in-chief of the “Journal of Mathematical Analysis and Applications”. Professor Krantz is currently the editor-in-chief of the AMS Notices and also edits for “The American Mathematical Monthly”, “Complex Analysis and Elliptical Equations”, and “The Bulletin of the American Mathematical Monthly”. Krantz is also known for his wide breadth of expertise in several areas of mathematics such as harmonica analysis, differential geometry, and Lie groups, to name a few. Notable awards include Chauvenet Prize (1992), Beckenbach Book Award (1994), Kemper Prize (1994), Outstanding Academic Book Award (1998), Washington University Faculty Mentor Award (2007).

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation