The entropy of the Angenent torus is approximately 1.85122

Autor:	Berchenko-Kogan, Yakov
Rok vydání:	2018
Předmět:	Mathematics - Differential Geometry Mathematics - Numerical Analysis 53C44 70H25 65-05 65Pxx
Druh dokumentu:	Working Paper
DOI:	10.1080/10586458.2019.1583616
Popis:	To study the singularities that appear in mean curvature flow, one must understand self-shrinkers, surfaces that shrink by dilations under mean curvature flow. The simplest examples of self-shrinkers are spheres and cylinders. In 1989, Angenent constructed the first nontrivial example of a self-shrinker, a torus. A key quantity in the study of the formation of singularities is the entropy, defined by Colding and Minicozzi based on work of Huisken. The values of the entropy of spheres and cylinders have explicit formulas, but there is no known formula for the entropy of the Angenent torus. In this work, we numerically estimate the entropy of the Angenent torus using the discrete Euler-Lagrange equations. Comment: 14 pages, 5 figures, Jupyter code included as ancillary file. Journal of Experimental Mathematics, 2019
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1808.08163 Zobrazit plný text záznamu View this record from Arxiv