scholarly journals The Curve Shortening Flow in the Metric-Affine Plane

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 701
Author(s):  
Vladimir Rovenski
Keyword(s):  
Classical Result ◽  
Affine Plane ◽  
Euclidean Plane ◽  
Geometric Condition ◽  
Convex Curve ◽  
Initial Curve ◽  
Curve Shortening Flow ◽  
Convex Curves ◽  
Curve Shortening ◽  
First Time

We investigated, for the first time, the curve shortening flow in the metric-affine plane and prove that under simple geometric condition (when the curvature of initial curve dominates the torsion term) it shrinks a closed convex curve to a “round point” in finite time. This generalizes the classical result by M. Gage and R.S. Hamilton about convex curves in a Euclidean plane.

scholarly journals Grid Peeling and the Affine Curve-Shortening Flow

2018 ◽  
Vol 29 (3) ◽  
pp. 306-316
Author(s):  
David Eppstein ◽  
Sariel Har-Peled ◽  
Gabriel Nivasch
Keyword(s):  
Curve Shortening Flow ◽  
Curve Shortening

Long-term Behavior of Curve Shortening Flow in $\mathbb{R}^3$

2020 ◽  
Vol 52 (2) ◽  
pp. 1221-1231
Author(s):  
Jiří Minarčík ◽  
Michal Beneš
Keyword(s):  
Curve Shortening Flow ◽  
Curve Shortening ◽  
Long Term Behavior

scholarly journals An Adaptive Moving Mesh Method for Forced Curve Shortening Flow

2019 ◽  
Vol 41 (2) ◽  
pp. A1170-A1200 ◽  
Author(s):  
J. A. Mackenzie ◽  
M. Nolan ◽  
C. F. Rowlatt ◽  
R. H. Insall
Keyword(s):  
Moving Mesh ◽  
Moving Mesh Method ◽  
Curve Shortening Flow ◽  
Mesh Method ◽  
Adaptive Moving Mesh Method ◽  
Curve Shortening
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