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POLYGON SHORTENING MAKES (MOST) QUADRILATERALS CIRCULAR

  • Published : 2002.02.01

Abstract

We show that an analog of the age-Grayson-Hamilton Theorem for curves moving according to their mean curvature holds for the motion of quadrilaterals according to their Menger curvature.

References

  1. Invent. Math. v.76 Curve shortening makes convex curves circular M. Gage https://doi.org/10.1007/BF01388602
  2. J. Differential Geometry v.26 The heat equation shrinking convex plane curves M. Gage;R.S. Hamilton
  3. J. Differential Geometry v.26 The heat equation shrinks embeded plane curves to round points M. A. Grayson https://doi.org/10.4310/jdg/1214441371
  4. Annals of Math. v.44 The Cauchy integral, analytic capacity, and uniform rectifiablity M. S. Melnikov;P. Mattila;J. Verdera https://doi.org/10.2307/2118585
  5. Transl., Ser. 2, Am. Math. Soc. v.180(34) Discrete versions of the four-vertex theorem, Topics in singularity theory. V.I. Arnold's 60th anniversary collection V. D. Sedykh;A. (ed.) et al. Khovanskij, editor

Cited by

  1. Asymptotic Behavior of $$\beta $$ β -Polygon Flows pp.1559-002X, 2017, https://doi.org/10.1007/s12220-017-9940-y
  2. Semidiscrete Geometric Flows of Polygons vol.114, pp.4, 2007, https://doi.org/10.1080/00029890.2007.11920419