mathematics, the curve-shortening flow is a process that modifies a smooth curve in the Euclidean plane by moving its points perpendicularly to the curve at a speed...

simplest context for curve shortening flow. Using the maximum principle as applied to the distance between two points on a curve, they proved that if...

identical with the curve shortening flow. The mean curvature flow is a different geometric flow which also has the curve shortening flow as a special case...

flow, as in soap films; critical points are minimal surfaces Curve-shortening flow, the one-dimensional case of the mean curvature flow Willmore flow...

the curve-shortening flow, a process for continuously moving the points of the curve towards their local centers of curvature. Applying this flow to the...

mean curvature flow. Related flows are: Curve-shortening flow, the one-dimensional case of mean curvature flow the surface tension flow the Lagrangian...

Ricci flow on each of these pieces. This procedure is known as Ricci flow with surgery. Perelman provided a separate argument based on curve shortening flow...

a shape is. The curve-shortening flow decreases the isoperimetric ratio of any smooth convex curve so that, in the limit as the curve shrinks to a point...

work on heat equations in Riemannian geometry. Caloric polynomial Curve-shortening flow Diffusion equation Relativistic heat conduction Schrödinger equation...

mean curvature flow. Its existence shows that, unlike the one-dimensional curve-shortening flow (for which every embedded closed curve converges to a...

only compact convex ancient solutions other than circles for the curve-shortening flow. Angenent was raised in Haarlem, the Netherlands. He obtained his...

convex curve, and greater than 2π whenever the curve has any non-convexities. When a smooth simple closed curve undergoes the curve-shortening flow, its...

at the University of Rochester. He is known for his work on the curve-shortening flow, and in particular for the Gage–Hamilton–Grayson theorem, proved...

isoperimetric problem is a zero wind speed case of Chaplygin problem Curve-shortening flow Expander graph Gaussian isoperimetric inequality Isoperimetric dimension...

of curves and surfaces under different processes that change them continuously. For instance, the curve-shortening flow is a process in which curves in...

Natasa (2010), "Classification of compact ancient solutions to the curve shortening flow", Journal of Differential Geometry, 84 (3): 455–464, arXiv:0806...

1 through 4 concern the heat equation and the curve-shortening flow defined from it, in which a curve moves in the Euclidean plane, perpendicularly to...

In the study of the curve-shortening flow, in which each point of a curve in the Euclidean plane moves perpendicularly to the curve, with speed proportional...

surface. Lyusternik–Fet theorem Theorem of the three geodesics Curve-shortening flow Selberg trace formula Selberg zeta function Zoll surface Besse,...

called the twisted majority rule. Symmetric under on-off reversal. Approximates the curve-shortening flow on the boundaries between live and dead cells....

speaking in the differential geometry section on the curve-shortening flow and mean curvature flow. In 2012, he was selected as one of the inaugural fellows...

irrelevant for analysis of the geometrization conjecture but uses curve-shortening flow to provide a simpler argument for the special case of the Poincaré...

Science Talent Search (Cunningham 2007). Curve-shortening flow, a continuous transformation of a closed curve in the plane that eventually convexifies...

solution was provided in the 1980s by Grayson, by means of the curve shortening flow A strengthened version of the theorem states that, on any Riemannian...

either straight or curved. The term hinge line has also been used for this feature. A fold surface seen perpendicular to its shortening direction can be...

Mathematica 164 (1990), no. 1–2, 29–71. C L Epstein, M Gage, The curve shortening flow. Wave motion: theory, modelling, and computation (Berkeley, Calif...

ventricle contracts in systole, there is longitudinal shortening (negative strain), circumferential shortening (negative strain) and transmural (wall) thickening...

In pathology, a contracture is a shortening of muscles, tendons, skin, and nearby soft tissues that causes the joints to shorten and become very stiff...

data can be used in a flow-versus-time graph. The area under the flow-versus-time curve for one cardiac cycle is the stroke volume. The length of the cardiac...

membraneous. During each cardiac cycle the interventricular septum contracts by shortening longitudinally and becoming thicker. The interventricular septum is the...