Lecture Notes on Mean Curvature Flow: Barriers and Singular Perturbations
Title | Lecture Notes on Mean Curvature Flow: Barriers and Singular Perturbations PDF eBook |
Author | Giovanni Bellettini |
Publisher | Springer |
Pages | 336 |
Release | 2014-05-13 |
Genre | Mathematics |
ISBN | 8876424296 |
The aim of the book is to study some aspects of geometric evolutions, such as mean curvature flow and anisotropic mean curvature flow of hypersurfaces. We analyze the origin of such flows and their geometric and variational nature. Some of the most important aspects of mean curvature flow are described, such as the comparison principle and its use in the definition of suitable weak solutions. The anisotropic evolutions, which can be considered as a generalization of mean curvature flow, are studied from the view point of Finsler geometry. Concerning singular perturbations, we discuss the convergence of the Allen–Cahn (or Ginsburg–Landau) type equations to (possibly anisotropic) mean curvature flow before the onset of singularities in the limit problem. We study such kinds of asymptotic problems also in the static case, showing convergence to prescribed curvature-type problems.
Lecture Notes on Mean Curvature Flow
Title | Lecture Notes on Mean Curvature Flow PDF eBook |
Author | Carlo Mantegazza |
Publisher | Springer Science & Business Media |
Pages | 175 |
Release | 2011-07-28 |
Genre | Mathematics |
ISBN | 3034801459 |
This book is an introduction to the subject of mean curvature flow of hypersurfaces with special emphasis on the analysis of singularities. This flow occurs in the description of the evolution of numerous physical models where the energy is given by the area of the interfaces. These notes provide a detailed discussion of the classical parametric approach (mainly developed by R. Hamilton and G. Huisken). They are well suited for a course at PhD/PostDoc level and can be useful for any researcher interested in a solid introduction to the technical issues of the field. All the proofs are carefully written, often simplified, and contain several comments. Moreover, the author revisited and organized a large amount of material scattered around in literature in the last 25 years.
Lecture Notes on Mean Curvature Flow
Title | Lecture Notes on Mean Curvature Flow PDF eBook |
Author | |
Publisher | |
Pages | 0 |
Release | 2011 |
Genre | |
ISBN |
Lectures on Mean Curvature Flows
Title | Lectures on Mean Curvature Flows PDF eBook |
Author | Xi-Ping Zhu |
Publisher | |
Pages | 150 |
Release | 2002 |
Genre | Flows |
ISBN | 9781470438210 |
"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 o.
Lectures on Mean Curvature Flow and Related Equations
Title | Lectures on Mean Curvature Flow and Related Equations PDF eBook |
Author | Tom Ilmanen (Mathématicien) |
Publisher | |
Pages | |
Release | 1998 |
Genre | |
ISBN |
Brakke's Mean Curvature Flow
Title | Brakke's Mean Curvature Flow PDF eBook |
Author | Yoshihiro Tonegawa |
Publisher | Springer |
Pages | 100 |
Release | 2019-04-09 |
Genre | Mathematics |
ISBN | 9811370753 |
This book explains the notion of Brakke’s mean curvature flow and its existence and regularity theories without assuming familiarity with geometric measure theory. The focus of study is a time-parameterized family of k-dimensional surfaces in the n-dimensional Euclidean space (1 ≤ k in
Mean Curvature Flow
Title | Mean Curvature Flow PDF eBook |
Author | Theodora Bourni |
Publisher | Walter de Gruyter GmbH & Co KG |
Pages | 149 |
Release | 2020-12-07 |
Genre | Mathematics |
ISBN | 3110618362 |
With contributions by leading experts in geometric analysis, this volume is documenting the material presented in the John H. Barrett Memorial Lectures held at the University of Tennessee, Knoxville, on May 29 - June 1, 2018. The central topic of the 2018 lectures was mean curvature flow, and the material in this volume covers all recent developments in this vibrant area that combines partial differential equations with differential geometry.