第123回

日時 Time

2025年1月6日（月）16:30〜18:00

場所 Place

自然科学５号館研究棟2階 209A室 + Zoom
Natural Science and Technology Hall 5, 2nd floor, Room 209A
Zoom registration: https://kanazawa-university.zoom.us/meeting/register/tZMtdeGprTItGdSVnSVyL2oVcqme0N4TEjkW

講演者 Speaker

Philip Schrader（Murdoch University）

タイトル Title

Curve shortening by Sobolev gradient flow

概要 Abstract

The classical curve shortening flow, or one-dimensional mean curvature flow, is the gradient descent of the length functional on curves when the gradient is taken with respect to a parametrisation invariant L^2 metric. In this talk I will discuss the gradient flows of length with respect to a family of parametrisation invariant Sobolev H^1 metrics with different degrees of homogeneity. The family of flows all turn out to be equivalent under time reparametrisations. Solutions preserve embeddedness, converge to points and appear to become round while converging, like the classical flow. But unlike the classical flow, we do not encounter singularities.