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

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

• Publisher: Birkhäuser Basel
• Year: 2004
• Tongue: English
• Leaves: 157
• Series: Progress in Nonlinear Differential Equations and Their Applications 59
• Edition: 1
• Category: Library

✦ Synopsis

This book collects invited contributions by specialists in the domain of elliptic partial differential equations and geometric flows. There are introductory survey articles as well as papers presenting the latest research results. Among the topics covered are blow-up theory for second order elliptic equations; bubbling phenomena in the harmonic map heat flow; applications of scans and fractional power integrands; heat flow for the p-energy functional; Ricci flow and evolution by curvature of networks of curves in the plane.

✦ 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

Functional Analysis; Partial Differential Equations; Differential Geometry