The shape of a figure-eight under the curve shortening flow.

Matthew A. Grayson

Displaying similar documents to “The shape of a figure-eight under the curve shortening flow.”

Zero-temperature 2D stochastic Ising model and anisotropic curve-shortening flow

Hubert Lacoin, François Simenhaus, Fabio Lucio Toninelli (2014)

Journal of the European Mathematical Society

Similarity:

Distinguishing Prymians from Jacobians.

V.V. Shokurov (1981/82)

Inventiones mathematicae

Similarity:

A projectively natural flow for circle diffeomorphisms.

Richard Schwartz (1992)

Inventiones mathematicae

Similarity:

Some Results on the Mordell-Weil Group of the Jacobian of the Fermat Curve.

David E. Rohrlich, Benedict H. Gross (1978)

Inventiones mathematicae

Similarity:

The area preserving curve shortening flow with Neumann free boundary conditions

Elena Mäder-Baumdicker (2015)

Geometric Flows

Similarity:

We study the area preserving curve shortening flow with Neumann free boundary conditions outside of a convex domain in the Euclidean plane. Under certain conditions on the initial curve the flow does not develop any singularity, and it subconverges smoothly to an arc of a circle sitting outside of the given fixed domain and enclosing the same area as the initial curve.

The monodromy of Weierstrass points.

D. Eisenbud, J. Harris (1987)

Inventiones mathematicae

Similarity:

Computational studies of conserved mean-curvature flow

Miroslav Kolář, Michal Beneš, Daniel Ševčovič (2014)

Mathematica Bohemica

Similarity:

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 unify the total/local-length-constraints of the gradient flow for the bending energy of plane curves

Yuki Miyamoto, Takeyuki Nagasawa, Fumito Suto (2009)

Kybernetika

Similarity:

The gradient flow of bending energy for plane curve is studied. The flow is considered under two kinds of constraints; one is under the area and total-length constraints; the other is under the area and local-length constraints. The fundamental results (the local existence and uniqueness) were obtained independently by Kurihara and the second author for the former one; by Okabe for the later one. For the former one the global existence was shown for any smooth initial curves, but the...