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El. knyga: Coulomb Frames in the Normal Bundle of Surfaces in Euclidean Spaces: Topics from Differential Geometry and Geometric Analysis of Surfaces

  • Formatas: PDF+DRM
  • Serija: Lecture Notes in Mathematics 2053
  • Išleidimo metai: 30-Jun-2012
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Kalba: eng
  • ISBN-13: 9783642298462
Kitos knygos pagal šią temą:
Coulomb Frames in the Normal Bundle of Surfaces in Euclidean Spaces: Topics from Differential Geometry and Geometric Analysis of SurfacesDidesnis paveikslėlis
  • Formatas: PDF+DRM
  • Serija: Lecture Notes in Mathematics 2053
  • Išleidimo metai: 30-Jun-2012
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Kalba: eng
  • ISBN-13: 9783642298462
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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.

Recenzijos

From the reviews:

This book is dedicated to students and young researchers interested in analysis, partial differential equations and differential geometry. All the material is structured in four chapters . These reflect the concerns of the author to produce an original, attractive and intelligent support for students with solid anchor in traditional courses of differential geometry and physics. Threads are complementary to traditional lectures, stimulating curiosity and desire for novelty. (Constantin Udrite, Zentralblatt MATH, Vol. 1264, 2013)

1 Surface Geometry
1(30)
1.1 Regular Surfaces
1(2)
1.2 Examples
3(3)
1.3 The Fundamental Forms
6(4)
1.4 Differential Equations
10(4)
1.5 Integrability Conditions
14(6)
1.6 The Curvature of the Normal Bundle
20(11)
2 Elliptic Systems
31(22)
2.1 The Mean Curvature Vector
31(5)
2.2 Curvature Estimates
36(17)
3 Normal Coulomb Frames in R4
53(22)
3.1 Torsion-Free Normal Frames for Curves and Surfaces
53(6)
3.2 Normal Coulomb Frames
59(2)
3.3 Constructing Normal Coulomb Frames, and Their Properties
61(2)
3.4 Estimating the Torsions of Normal Coulomb Frames
63(9)
3.5 An Example: Holomorphic Graphs
72(3)
4 Normal Coulomb Frames in Rn+2
75(32)
4.1 Problem Formulation
75(1)
4.2 The Euler-Lagrange Equations
76(4)
4.3 Examples
80(1)
4.4 Quadratic Growth in the Gradient
81(2)
4.5 Torsion-Free Normal Frames
83(4)
4.6 Non-flat Normal Bundles
87(3)
4.7 Bounds for the Total Torsion
90(2)
4.8 Existence and Regularity of Weak Normal Coulomb Frames
92(11)
4.9 Classical Regularity of Normal Coulomb Frames
103(4)
References 107(6)
List of Names 113(2)
Index 115
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