This book is the first monograph dedicated entirely to Willmore energy and Willmore surfaces as contemporary topics in differential geometry. While it focuses on Willmore energy and related conjectures, it also sits at the intersection between integrable systems, harmonic maps, Lie groups, calculus of variations, geometric analysis and applied differential geometry.
Rather than reproducing published results, it presents new directions, developments and open problems. It addresses questions like: What is new in Willmore theory? Are there any new Willmore conjectures and open problems? What are the contemporary applications of Willmore surfaces?
As well as mathematicians and physicists, this book is a useful tool for postdoctoral researchers and advanced graduate students working in this area.
Table of Contents
Willmore Energy: Brief Introduction and Survey. Transformations of Generalized Harmonic bundles and Constrained Willmore Surfaces. Analytical Representations of Willmore and Generalized Willmore Surfaces. Construction of Willmore Two-Spheres Via Harmonic Maps Into SO+(1;n + 3)=(SO+(1; 1) SO(n + 2)). Towards a Constrained Willmore Conjecture
Magdalena Toda holds a PhD in Mathematics from University of Kansas and a PhD in Applied Mathematics from University Politehnica Bucharest. She is currently a Professor of Mathematics at Texas Tech University, where she has served as interim chairperson between 2015-2016, and as department chairperson since 2016. She has published over 30 articles in academic journals on topics including surface theory and geometric solutions of non-linear partial differential equations. Over the past decade she has mainly studied fluid flows from a geometric viewpoint. Willmore-type energies represent one of her most recent interests.