Buch, Englisch, Format (B × H): 187 mm x 262 mm, Gewicht: 489 g
Buch, Englisch, Format (B × H): 187 mm x 262 mm, Gewicht: 489 g
ISBN: 978-0-8218-3311-7
Verlag: American Mathematical Society
``Mean curvature flow' is a term that is used to describe the evolution of a hypersurface whose normal velocity is given by the mean curvature. In the simplest case of a convex closed curve on the plane, the properties of the mean curvature flow are described by Gage-Hamilton's theorem. This theorem states that under the mean curvature flow, the curve collapses to a point, and if the flow is diluted so that the enclosed area equals $\pi$, the curve tends to the unit circle. In this book, the author gives a comprehensive account of fundamental results on singularities and the asymptotic behavior of mean curvature flows in higher dimensions. Among other topics, he considers in detail Huisken's theorem (a generalization of Gage-Hamilton's theorem to higher dimension), evolution of non-convex curves and hypersurfaces, and the classification of singularities of the mean curvature flow. Because of the importance of the mean curvature flow and its numerous applications in differential geometry and partial differential equations, as well as in engineering, chemistry, and biology, this book can be useful to graduate students and researchers working in these areas. The book would also make a nice supplementary text for an advanced course in differential geometry. Prerequisites include basic differential geometry, partial differential equations, and related applications.
Fachgebiete
- Mathematik | Informatik Mathematik Topologie Algebraische Topologie
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
- Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
