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Geometric Analysis and Nonlinear Partial Differential Equations

  • Book
  • © 2003

Overview

Editors:
  1. Stefan Hildebrandt

    1. Department of Mathematics, University of Bonn, Bonn, Germany

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    You can also search for this editor in PubMed   Google Scholar

  2. Hermann Karcher

    1. Department of Mathematics, University of Bonn, Bonn, Germany

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    You can also search for this editor in PubMed   Google Scholar

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Table of contents (34 chapters)

  1. Front Matter

    Pages I-IX
    Download chapter PDF

  2. Olga Ladyzhenskaya

    1. Olga Ladyzhenskaya

      • Michael Struwe
      Pages 1-10

  3. Geometric Analysis and Calculus of Variations

    1. Front Matter

      Pages 11-11
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    2. On the Spectral Theory of Surfaces with Cusps

      • Werner Ballmann, Jochen Brüning
      Pages 13-37

    3. The Dirac Determinant of Spherical Space Forms

      • Christian Bär, Sven Schopka
      Pages 39-67

    4. Constructing Isospectral Metrics via Principal Connections

      • Dorothee Schueth
      Pages 69-79

    5. Parametrizations of Teichmüller Space and Its Thurston Boundary

      • Ursula Hamenstädt
      Pages 81-88

    6. Linearization of Isotropic Automorphisms of Non-quadratic Elliptic CR-Manifolds in ℂ4

      • Vladimir V. Ežov, Gerd Schmalz
      Pages 89-103

    7. Global C 2+α-Estimates for Conformai Maps

      • Friedrich Sauvigny
      Pages 105-115

    8. On Karcher’s Twisted Saddle Towers

      • Matthias Weber
      Pages 117-127

    9. Unstable Periodic Discrete Minimal Surfaces

      • Konrad Polthier
      Pages 129-145

    10. An Adaptive Finite Element Method for Minimal Surfaces

      • W. Dörfler, K. G. Siebert
      Pages 147-175

    11. Singular Minimal Surfaces

      • Ulrich Dierkes
      Pages 177-193

    12. Note on the Isoperimetric Profile of a Convex Body

      • Ernst Kuwert
      Pages 195-200

    13. Geometric Conditions on Free Boundaries

      • Reiner Schätzte
      Pages 201-216

    14. On Generalized Mean Curvature Flow in Surface Processing

      • Ulrich Clarenz, Gerhard Dziuk, Martin Rumpf
      Pages 217-248

    15. A Finite Element Level Set Method for Anisotropic Mean Curvature Flow with Space Dependent Weight

      • Klaus Deckelnick, Gerhard Dziuk
      Pages 249-264

    16. Optimal Regularity Results via A-Harmonic Approximation

      • Frank Duzaar, Joseph F. Grotowski, Klaus Steffen
      Pages 265-296

    17. Dominance Functions for Parametric Lagrangians

      • Stefan Hildebrandt, Heiko von der Mosel
      Pages 297-326

    18. Convex Variational Problems with Linear Growth

      • Michael Bildhauer, Martin Fuchs
      Pages 327-344
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Keywords

About this book

This book is not a textbook, but rather a coherent collection of papers from the field of partial differential equations. Nevertheless we believe that it may very well serve as a good introduction into some topics of this classical field of analysis which, despite of its long history, is highly modem and well prospering. Richard Courant wrote in 1950: "It has always been a temptationfor mathematicians to present the crystallized product of their thought as a deductive general theory and to relegate the individual mathematical phenomenon into the role of an example. The reader who submits to the dogmatic form will be easily indoctrinated. Enlightenment, however, must come from an understanding of motives; live mathematical development springs from specific natural problems which can be easily understood, but whose solutions are difficult and demand new methods or more general significance. " We think that many, if not all, papers of this book are written in this spirit and will give the reader access to an important branch of analysis by exhibiting interest­ ing problems worth to be studied. Most of the collected articles have an extensive introductory part describing the history of the presented problems as well as the state of the art and offer a well chosen guide to the literature. This way the papers became lengthier than customary these days, but the level of presentation is such that an advanced graduate student should find the various articles both readable and stimulating.

Editors and Affiliations

  • Department of Mathematics, University of Bonn, Bonn, Germany

    Stefan Hildebrandt, Hermann Karcher

Bibliographic Information

  • Book Title: Geometric Analysis and Nonlinear Partial Differential Equations

  • Editors: Stefan Hildebrandt, Hermann Karcher

  • DOI: https://doi.org/10.1007/978-3-642-55627-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2003

  • Hardcover ISBN: 978-3-540-44051-2Published: 01 November 2002

  • Softcover ISBN: 978-3-642-62887-0Published: 03 October 2013

  • eBook ISBN: 978-3-642-55627-2Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: IX, 673

  • Number of Illustrations: 151 b/w illustrations

  • Topics: Partial Differential Equations

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