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.
