Coulomb Frames in the Normal Bundle of Surfaces in Euclidean Spaces

Topics from Differential Geometry and Geometric Analysis of Surfaces

  • Steffen Fröhlich

Part of the Lecture Notes in Mathematics book series (LNM, volume 2053)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Steffen Fröhlich
    Pages 1-29
  3. Steffen Fröhlich
    Pages 31-52
  4. Steffen Fröhlich
    Pages 53-73
  5. Steffen Fröhlich
    Pages 75-105
  6. Back Matter
    Pages 107-117

About this book

Introduction

This book is intended for advanced students and young researchers interested in the analysis of partial differential equations and differential geometry. It discusses elementary concepts of surface geometry in higher-dimensional Euclidean spaces, in particular the differential equations of Gauss-Weingarten together with various integrability conditions and corresponding surface curvatures. It includes a chapter on curvature estimates for such surfaces, and, using results from potential theory and harmonic analysis, it addresses geometric and analytic methods to establish the existence and regularity of Coulomb frames in their normal bundles, which arise as critical points for a functional of total torsion.

Keywords

53A07, 53A10, 35J15, 35J47, 30G20. curvature estimates elementary differential geometry normal Coulomb frames twodimensional surfaces in Euclidean spaces

Authors and affiliations

  • Steffen Fröhlich
    • 1
  1. 1.Department of Physics, Mathematics,, Computer SciencesJohannes Gutenberg UniversityMainzGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-29846-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2012
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-29845-5
  • Online ISBN 978-3-642-29846-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book
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