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Coulomb Frames in the Normal Bundle of Surfaces in Euclidean Spaces: Topics From Differential Geometry and Geometric Analysis of Surfaces

Steffen Fröhlich
Format
Book
Published
Heidelberg ; New York : Springer Verlag, 2012.
Language
English
Series
Lecture Notes in Mathematics
Lecture Notes in Mathematics (Springer-Verlag)
ISBN
9783642298455, 3642298451
Summary
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.
Contents
  • Surface geometry
  • Elliptic systems
  • Normal Coulomb frames in R⁴
  • Normal Coulomb frames in Rn"⁺²
Description
xiv, 117 p. : ill. ; 23 cm.
Notes
Includes bibliographical references (p. 107-111) and index.
Series Statement
Lecture notes in mathematics ; 2053
Lecture notes in mathematics (Springer-Verlag) 2053
Technical Details
  • Access in Virgo Classic
  • Staff View

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    a| Coulomb frames in the normal bundle of surfaces in Euclidean spaces : b| topics from differential geometry and geometric analysis of surfaces / c| Steffen Fröhlich.
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    a| Heidelberg ; a| New York : b| Springer Verlag, c| 2012.
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    a| xiv, 117 p. : b| ill. ; c| 23 cm.
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    a| Lecture notes in mathematics ; v| 2053
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    a| Includes bibliographical references (p. 107-111) and index.
    505
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    a| Surface geometry -- Elliptic systems -- Normal Coulomb frames in R⁴ -- Normal Coulomb frames in Rn"⁺²
    520
      
      
    a| 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.
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