Geometric Analysis of the Bergman Kernel and Metric

  • Steven G.┬áKrantz

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

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Steven G. Krantz
    Pages 1-69
  3. Steven G. Krantz
    Pages 71-85
  4. Steven G. Krantz
    Pages 87-116
  5. Steven G. Krantz
    Pages 117-145
  6. Steven G. Krantz
    Pages 147-186
  7. Steven G. Krantz
    Pages 187-250
  8. Steven G. Krantz
    Pages 251-271
  9. Steven G. Krantz
    Pages 273-273
  10. Back Matter
    Pages 275-292

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.


Bergman kernel Bergman metric Bergman theory applications to Bergman holomorphic mapping integral formulas invariant metrics reproducing kernels

Authors and affiliations

  • Steven G.┬áKrantz
    • 1
  1. 1.Department of MathematicsWashington University in St. LouisSt. LouisUSA

Bibliographic information