Regularity Theory for Mean Curvature Flow

Klaus Ecker (Autor)

Buch | Softcover

165 Seiten

2004 | Softcover reprint of the original 1st ed. 2004
Birkhauser Boston Inc (Verlag)
978-0-8176-3781-1 (ISBN)

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Mean curvature flow and related geometric evolution equations are important tools in mathematics and mathematical physics. This title deals with the motion of surfaces for which the normal velocity at every point is given by the mean curvature at that point.

Mean curvature flow and related flows are important tools in mathematics and mathematical physics. For example, the famous Penrose conjecture in general relativity by Huisken and Ilmanan was based on a curvature flow approach. Under mean curvature flow, surfaces usually develop singularities in finite time. This book presents techniques in the study of singularities of mean curvature flow. It details the influential work of K. Brakke as well as such recent developments as relations to regularity theory for minimal surfaces, as in Allard's and de Giorgi's work.

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.

Reihe/Serie	Progress in Nonlinear Differential Equations and Their Applications ; 57
Zusatzinfo	XIII, 165 p.
Verlagsort	Secaucus
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-8176-3781-8 / 0817637818
ISBN-13	978-0-8176-3781-1 / 9780817637811
Zustand	Neuware