Regularity Theory for Mean Curvature Flow
Edition: 1 edition
Publisher: Birkhäuser Boston
Published: July 13, 2004
Language: eng
Format: Paperback
Number of pages: 144
ISBN-13: 9780817637811
Subjects: Differential & Riemannian geometry; Science/Mathematics; Mathematics; Geometry - Differential; Mathematics / Geometry / Differential; Mathematical Analysis
First sentence: Mean curvature flow evolves hypersurfaces in their normal direction with speed equal to the mean curvature at each point.
Description: This work is devoted to the motion of surfaces for which the normal velocity at every point is given by the mean curvature at that point; this geometric heat flow process is called mean curvature flow. Mean curvature flow and related geometric evolution equations are important tools in mathematics and mathematical physics. A major example is Hamilton's Ricci flow program, which has the aim of settling Thurston's geometrization conjecture, with recent major progress due to Perelman. Another important application of a curvature flow process is the resolution of the famous Penrose conjecture in general relativity by Huisken and Ilmanen. Under mean curvature flow, surfaces usually develop singularities in finite time. This work presents techniques for the study of singularities of mean curvature flow and is largely based on the work of K. Brakke, although more recent developments are incorporated.