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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.
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 Udriste, Zentralblatt MATH, Vol. 1264, 2013)
"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 Udriste, Zentralblatt MATH, Vol. 1264, 2013)