Brakke The Motion of a Surface by Its Mean Curvature

1. Auflage 2015
ISBN: 978-1-4008-6743-1
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 258 Seiten

Reihe: Mathematical Notes

Kenneth Brakke studies in general dimensions a dynamic system of surfaces of no inertial mass driven by the force of surface tension and opposed by a frictional force proportional to velocity. He formulates his study in terms of varifold surfaces and uses the methods of geometric measure theory to develop a mathematical description of the motion of a surface by its mean curvature. This mathematical description encompasses, among other subtleties, those of changing geometries and instantaneous mass losses.

Originally published in 1978.

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Autoren/Hrsg.

Brakke, Kenneth A.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie

Inhaltsverzeichnis

Frontmatter, pg. i
Table of Contents, pg. iii
1. Introduction, pg. 1
2. Preliminaries, pg. 6
3. Motion by mean curvature, pg. 18
4. Existence of varifolds moving by their mean curvature, pg. 33
5. Perpendicularity of mean curvature, pg. 121
6. Regularity, pg. 161
Appendix A: Grain growth in metals, pg. 224
Appendix B: Curves in R2, pg. 229
Appendix C: Curves of constant shape, pg. 235
Appendix D: Density bounds and rectiflability, pg. 238
Figure captions, pg. 240
Figures, pg. 241
References, pg. 251