Regularity Theory for Mean Curvature Flow

2004. Auflage 2003
ISBN: 978-0-8176-3243-4
Verlag: Springer

Buch, Englisch, Band 57, 165 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 435 g

Reihe: Progress in Nonlinear Differential Equations and Their Applications

* 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.

Zielgruppe

Research

Autoren/Hrsg.

Ecker, Klaus

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

1 Introduction.- 2 Special Solutions and Global Behaviour.- 3 Local Estimates via the Maximum Principle.- 4 Integral Estimates and Monotonicity Formulas.- 5 Regularity Theory at the First Singular Time.- A Geometry of Hypersurfaces.- B Derivation of the Evolution Equations.- C Background on Geometric Measure Theory.- D Local Results for Minimal Hypersurfaces.- E Remarks on Brakke¡¯s Clearing Out Lemma.- F Local Monotonicity in Closed Form.