Variational Problems in Riemannian Geometry: Bubbles, Scans and Geometric Flows

✍ Scribed by Paul Baird, Ahmad El Soufi, Ali Fardoun, Rachid Regbaoui (eds.)

• Publisher: Birkhäuser, Birkhäuser Basel, Imprint
• Year: 2004
• Tongue: English
• Leaves: 157
• Series: Progress in nonlinear differential equations and their applications 59
• Edition: Softcover reprint of the original 1st ed. 2004
• Category: Library

✦ Synopsis

This volume has grown from a conference entitled Harmonic Maps, Minimal Sur- faces and Geometric Flows which was held at the Universite de Bretagne Occi- dentale from July 7th-12th, 2002, in the town of Brest in Brittany, France. We welcomed many distinguished mathematicians from around the world and a dy- namic meeting took place, with many fruitful exchanges of ideas. In order to produce a work that would have lasting value to the mathematical community, the organisers decided to invite a small number of participants to write in-depth articles around a common theme. These articles provide a balance between introductory surveys and ones that present the newest results that lie at the frontiers of research. We thank these mathematicians, all experts in their field, for their contributions. Such meetings depend on the support of national organisations and the local community and we would like to thank the following: the Ministere de l'Education Nationale, Ministere des Affaires Etrangeres, Centre National de Recherche Sci en- tifique (CNRS), Conseil Regional de Bretagne, Conseil General du Finistere, Com- munaute Urbaine de Brest, Universite de Bretagne Occidentale (UBO), Faculte des Sciences de l'UBO, Laboratoire de Mathematiques de l'UBO and the Departement de Mathematiques de l'UBO. Their support was generous and ensured the success of the meeting. We would also like to thank the members of the scientific committee for their advice and for their participation in the conception and composition of this volume: Pierre Berard, Jean-Pierre Bourguignon, Frederic Helein, Seiki Nishikawa and Franz Pedit

✦ Table of Contents

Front Matter....Pages i-xvii
Front Matter....Pages 1-1
Bubbles over Bubbles: A C 0 -theory for the Blow-up of Second Order Elliptic Equations of Critical Sobolev Growth....Pages 3-17
Application of Scans and Fractional Power Integrands....Pages 19-31
Bubbling of Almost-harmonic Maps between 2-spheres at Points of Zero Energy Density....Pages 33-42
Front Matter....Pages 43-43
Heat Flow into Spheres for a Class of Energies....Pages 45-65
Singularity Models for the Ricci Flow: An Introductory Survey....Pages 67-80
A Family of Expanding Ricci Solitons....Pages 81-93
Evolution by Curvature of Networks of Curves in the Plane....Pages 95-109
Front Matter....Pages 111-111
Harmonic Maps in Complex Finsler Geometry....Pages 113-132
Regularity of Harmonic Maps from a Flat Complex....Pages 133-148
Back Matter....Pages 149-150

✦ Subjects

Mathematics;Functional analysis;Differential equations, Partial;Global differential geometry