Geometric Analysis and Nonlinear Partial Differential Equations

1. Front Matter

   Pages I-IX

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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

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.

• Kolmogorov–Arnold–Moser theorem
• differential equation
• geometric analysis
• nonlinear partial differential equation
• nonlinear partial differential equations
• partial differential equation
• partial differential equations

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

  Stefan Hildebrandt, Hermann Karcher

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