Variational Problems in Riemannian Geometry

'This book is devoted to the study of maps and metrics that arise as extremals of a variational problem. Solutions, in general, satisfy in elliptic partial differential equation and can often be obtained by deformation under a geometric flow. The work particularly concentrates on singular behaviour, such as bubbling phenomena and the formation of solutions in the harmonic map flow and Ricci flow, respectively.' 'The articles provide a balance between introductory surveys and the most recent research, with a unique perspective on singular phenomena. Notions such as scans and the study of the evolution by curvature of networks of curves are completely new and lead the reader to the frontiers of the domain.' The intended readership are postgraduate students and researchers in the fields of elliptic and parabolic partial differential equations that arise from variational problems as well as researchers in related fields, such as particle physics and optimization.