On Yau's problem of evolving one curve to another: Convex case

摘要

A revised Yau's Curvature Difference Flow is considered to deform one convex curve X-0 to another one (X) over tilde. It is proved that this flow exists globally on time interval [0, +infinity) and the evolving curve, preserving its convexity and bounded area A, converges to a fixed limiting curve X-infinity(congruent to root A/(A) over tilde (X) over tilde) as time tends to infinity, where (A) over tilde is the area bounded by the target curve (X) over tilde. (C) 2018 Elsevier Inc. All rights reserved.