Lectures on Geometric Variational Problems

  • Seiki Nishikawa
  • Richard Schoen

Table of contents

  1. Front Matter
    Pages II-VIII
  2. An Introduction to Geometric Variational Problems

    1. Front Matter
      Pages 1-1
    2. Seiki Nishikawa, Richard Schoen
      Pages 2-9
    3. Seiki Nishikawa, Richard Schoen
      Pages 10-29
  3. Geometry of Gauge Fields

    1. Kenji Fukaya
      Pages 43-114
  4. Theorems on the Regularity and Singularity of Minimal Surfaces and Harmonic Maps

  5. Back Matter
    Pages 151-154

About this book


In this volume are collected notes of lectures delivered at the First In­ ternational Research Institute of the Mathematical Society of Japan. This conference, held at Tohoku University in July 1993, was devoted to geometry and global analysis. Subsequent to the conference, in answer to popular de­ mand from the participants, it was decided to publish the notes of the survey lectures. Written by the lecturers themselves, all experts in their respective fields, these notes are here presented in a single volume. It is hoped that they will provide a vivid account of the current research, from the introduc­ tory level up to and including the most recent results, and will indicate the direction to be taken by future researeh. This compilation begins with Jean-Pierre Bourguignon's notes entitled "An Introduction to Geometric Variational Problems," illustrating the gen­ eral framework of the field with many examples and providing the reader with a broad view of the current research. Following this, Kenji Fukaya's notes on "Geometry of Gauge Fields" are concerned with gauge theory and its applications to low-dimensional topology, without delving too deeply into technical detail. Special emphasis is placed on explaining the ideas of infi­ nite dimensional geometry that, in the literature, are often hidden behind rigorous formulations or technical arguments.


Eigenvalue Floer homology Geometric Variational Problems Guage theory Harmonic maps Laplace operator Minimal surface Smooth function compactness curvature manifold minimum singularity variational problem variational problems

Editors and affiliations

  • Seiki Nishikawa
    • 1
  • Richard Schoen
    • 2
  1. 1.Mathematical InstituteTohoku UniversitySendaiJapan
  2. 2.Department of MathematicsStanford UniversityStanfordUSA

Bibliographic information