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
New London, Wisconsin

Files

eithun discrete_csf.pdf

Citation

Mitchell Eithun , “Go With the Flow: Classifying the Asymptotic Behaviors of Semidiscrete Curve-Shortening Flows by Mitchell Eithun,” Senior Showcase Digital Collection, accessed November 20, 2018, https://rcseniorshowcase.omeka.net/items/show/65.

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