Displaying similar documents to “Mean curvature flow and self-similar submanifolds”

Introduction to mean curvature flow

Roberta Alessandroni (2008-2009)

Séminaire de théorie spectrale et géométrie

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This is a short overview on the most classical results on mean curvature flow as a flow of smooth hypersurfaces. First of all we define the mean curvature flow as a quasilinear parabolic equation and give some easy examples of evolution. Then we consider the M.C.F. on convex surfaces and sketch the proof of the convergence to a round point. Some interesting results on the M.C.F. for entire graphs are also mentioned. In particular when we consider the case of dimension one, we can compute...

Computational studies of conserved mean-curvature flow

Miroslav Kolář, Michal Beneš, Daniel Ševčovič (2014)

Mathematica Bohemica

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The paper presents the results of numerical solution of the evolution law for the constrained mean-curvature flow. This law originates in the theory of phase transitions for crystalline materials and describes the evolution of closed embedded curves with constant enclosed area. It is reformulated by means of the direct method into the system of degenerate parabolic partial differential equations for the curve parametrization. This system is solved numerically and several computational...

How to produce a Ricci flow via Cheeger–Gromoll exhaustion

Esther Cabezas-Rivas, Burkhard Wilking (2015)

Journal of the European Mathematical Society

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We prove short time existence for the Ricci flow on open manifolds of non-negative complex sectional curvature without requiring upper curvature bounds. By considering the doubling of convex sets contained in a Cheeger–Gromoll convex exhaustion and solving the singular initial value problem for the Ricci flow on these closed manifolds, we obtain a sequence of closed solutions of the Ricci flow with non-negative complex sectional curvature which subconverge to a Ricci flow on the open...

Gaussian curvature based tangential redistribution of points on evolving surfaces

Medľa, Matej, Mikula, Karol

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There exist two main methods for computing a surface evolution, level-set method and Lagrangian method. Redistribution of points is a crucial element in a Lagrangian approach. In this paper we present a point redistribution that compress quads in the areas with a high Gaussian curvature. Numerical method is presented for a mean curvature flow of a surface approximated by quads.