Go With the Flow: Classifying the Asymptotic Behaviors of Semidiscrete Curve-Shortening Flows by Mitchell Eithun
Mathematics
A semidiscrete curve-shortening flow continuously deforms a polygon in the direction of an inward normal until it shrinks to a point. We are interested in the long-time behavior of polygons under such flows. Is there a semidiscrete flow under which all polygons become asymptotically regular? This is an open question, but we provide numerical evidence to suggest that the recent β-polygon flow of Glickenstein and Liang produces regular polygons. It is known that triangles become regular under the β-polygon flow. Using a rescaled flow in which a regular polygon is a fixed point, we note how side lengths and angles evolve under the β-polygon flow and conjecture that all quadrilaterals become rhombic and polygons with more than 5 vertices become regular.
Mitchell Eithun
Senior Showcase Oral Presentation
Ripon College
April 18, 2017
The author reserves all rights.
Majors: Mathematics and Computer Science
Minor: Music
New London, Wisconsin