Coulomb frames in the normal bundle of surfaces in euclidean spaces : topics from differential geometry and geometric analysis of surfaces / Steffen Fröhlich.Material type: TextSeries: Lecture notes in mathematics (Springer-Verlag) ; 2053.Publication details: Berlin ; New York : Springer, ©2012. Description: 1 online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783642298462; 364229846X; 3642298451; 9783642298455Subject(s): Geometry, Differential | Frames (Combinatorial analysis) | Frames (Combinatorial analysis) | Geometry, Differential | Mathematics | Functions of complex variables | Differential equations, partial | Global differential geometry | Differential Geometry | Partial Differential EquationsGenre/Form: Electronic books. Additional physical formats: No titleDDC classification: 516.3/6 LOC classification: QA641 | .F76 2012Online resources: Click here to access online
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Surface Geometry -- Elliptic Systems -- Normal Coulomb Frames in \mathbbR4R4 -- Normal Coulomb Frames in \mathbbRn+2Rn+2.
Includes bibliographical references and index.
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.