This book offers an essential overview of computational conformal geometry applied to fundamental problems in specific engineering fields. It introduces readers to conformal geometry theory and discusses implementation issues from an engineering perspective. The respective chapters explore fundamental problems in specific fields of application, and detail how computational conformal geometric methods can be used to solve them in a theoretically elegant and computationally efficient way. The fields covered include computer graphics, computer vision, geometric modeling, medical imaging, and wireless sensor networks. Each chapter concludes with a summary of the material covered and suggestions for further reading, and numerous illustrations and computational algorithms complement the text. The book draws on courses given by the authors at the University of Louisiana at Lafayette, the State University of New York at Stony Brook, and Tsinghua University, and will be of interest to senior undergraduates, graduates and researchers in computer science, applied mathematics, and engineering.
In this original text, prolific mathematics author Steven G. Krantz addresses conformal geometry, a subject that has occupied him for four decades and for which he helped to develop some of the modern theory.
This book is an introduction to the theory of spatial quasiregular mappings intended for the uninitiated reader. At the same time the book also addresses specialists in classical analysis and, in particular, geometric function theory.
conformal. geometry. We showed in Part 1 that E ( 2 ) is Möbius invariant . In Part 2 , we show that the integrand of E ( 2 ) can be interpreted from a conformal geometric viewpoint . This viewpoint provides a new interpretation of ...
One of the most beautiful results in classical complex analysis that has a great appeal to geometry is the solution by F. Klein and H. ... However, they are all particular cases of the more general conformal geometry, that is the ( S 2, ...
We recall the geometric proof of Obata's Uniqueness Theorem on Sn : If R , const . on S " , then | E | = 0 and g ** ( gc ) for some = conformal transformation : Sn — Sn . For simplicity we 10. Deforming 02 to a constant function 83.
The goal is to construct conformal field theories in the geometric formulation, including the higher-genus parts, from vertex operator algebras, modules and intertwining operators. Recently there have been many works on operads and ...
Felix Klein's Erlangen Program lays out a blueprint for understanding a geometry by way of the group of mappings that preserve ... For complex function theory, Klein's idea may be implemented by means of the study of conformal mappings.
Authors should follow instructions listed on the Initial Submission page found at www.ams.org/memo/memosubmit.html. Algebra, to MICHAEL LARSEN, Department of Mathematics, Rawles Hall, Indiana University, 831 E 3rd Street, Bloomington, ...
All the techniques — including the geometric techniques used by Aubin [Aubin (1976)], Scho ̄en [Scho ̄en (1988)], Scho ̄en and Yau [Scho ̄en and Yau ... Up be p (possibly 2 Recent Progress in Conformal Geometry 1.2 Results and Conditions.
... h with dh 1w - dH and suitable initial conditions is in Im H = R. To summarize Theorem 9 (Richter [11]). Let ... Then the isotropic lines form an S'C HP', while the two complemen-.tary discs inherit complete hyperbolic metrics.