The Curve Shortening Problem

288 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Projective Differential Geometry Old and New: From the Schwarzian Derivative to the Cohomology of Diffeomorphism Groups (2004, background): “Curve shortening problems has been thoroughly studied in the recent years, see [42].”
On a non-local curve evolution problem in the plane (2008, background): “Since the changing of the tangential components of the velocity vector Xt affects only the parameterization, not the geometric shapes of the evolving curve (see, for example, [7, 11,12] or [23]), one may choose a suitable tangential component α = α(u, t) so that the geometric analysis of the evolvin”
A non-local area preserving curve flow (2009, methodology): “Our research is motivated by the famous works of Gage and Hamilton [9] and [4] (see also [3] for background and more results).”
On the planar dual Minkowski problem (2018, background): “There is a vast body of literature concerning the planar Lp-Minkowski problem [1, 3, 5, 15, 18, 19, 20, 21, 48, 49, 50].”
Rotationally symmetric solutions to the L p -Minkowski problem (2013, background): “It describes self-similar solutions to the anisotropic curve shortening flow [3,10].”
Classification of limiting shapes for isotropic curve flows (2002, background): “The first statement is also proved in [9].”
Mean Curvature Flow in Higher Codimension: Introduction and Survey (2011, unknown): “For the curve shortening flow see [22].”