ﻻ يوجد ملخص باللغة العربية
A recent article by the first two authors together with B Andrews and V-M Wheeler considered the so-called `ideal curve flow, a sixth order curvature flow that seeks to deform closed planar curves to curves with least variation of total geodesic curvature in the $L^2$ sense. Critical in the analysis there was a length bound on the evolving curves. It is natural to suspect therefore that the length-constrained ideal curve flow should permit a more straightforward analysis, at least in the case of small initial `energy. In this article we show this is indeed the case, with suitable initial data providing a flow that exists for all time and converges smoothly and exponentially to a multiply-covered round circle of the same length and winding number as the initial curve.
We show that any initial closed curve suitably close to a circle flows under length-constrained curve diffusion to a round circle in infinite time with exponential convergence. We provide an estimate on the total length of time for which such curves
We define and study a discrete process that generalizes the convex-layer decomposition of a planar point set. Our process, which we call homotopic curve shortening (HCS), starts with a closed curve (which might self-intersect) in the presence of a se
In this paper, we consider a new length preserving curve flow for convex curves in the plane. We show that the global flow exists, the area of the region bounded by the evolving curve is increasing, and the evolving curve converges to the circle in C-infinity topology as t goes to infinity.
In this paper we study an experimentally-observed connection between two seemingly unrelated processes, one from computational geometry and the other from differential geometry. The first one (which we call grid peeling) is the convex-layer decomposi
We will give a new proof of the existence of hypercylinder expander of the inverse mean curvature flow which is a radially symmetric homothetic soliton of the inverse mean curvature flow in $mathbb{R}^ntimes mathbb{R}$, $nge 2$, of the form $(r,y(r))