Go With the Flow: Classifying the Asymptotic Behaviors of Semidiscrete Curve-Shortening Flows by Mitchell Eithun
Dublin Core
Title
Go With the Flow: Classifying the Asymptotic Behaviors of Semidiscrete Curve-Shortening Flows by Mitchell Eithun
Subject
Mathematics
Description
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.
Creator
Mitchell Eithun
Source
Senior Showcase Oral Presentation
Publisher
Ripon College
Date
April 18, 2017
Rights
The author reserves all rights.
Identifier
Majors: Mathematics and Computer Science
Minor: Music
Minor: Music
New London, Wisconsin
Files
Collection
Citation
Mitchell Eithun , “Go With the Flow: Classifying the Asymptotic Behaviors of Semidiscrete Curve-Shortening Flows by Mitchell Eithun,” Senior Showcase Digital Collection, accessed March 21, 2023, https://rcseniorshowcase.omeka.net/items/show/65.