Math @ Duke

Publications [#265139] of Guillermo Sapiro
Papers Published
 SAPIRO, G, On affine plane curve evolution,
J. of Functional Analysis, vol. 119 no. 1
(1994),
pp. 79120, Elsevier BV, ISSN 00221236 [doi]
(last updated on 2019/06/24)
Abstract: An affine invariant curve evolution process is presented in this work. The evolution studied is the affine analogue of the Euclidean Curve Shortening flow. Evolution equations, for both affine and Euclidean invariants, are developed. An affine version of the classical (Euclidean) isoperimetric inequality is proved. This inequality is used to show that in the case of affine evolution of convex plane curves, the affine isoperimetric ratio is a nondecreasing function of time. Convergence of this affine isoperimetric ratio to the ellipse′s value (8π2), as well as convergence, in the Hausdorff metric, of the evolving curve to an ellipse, is also proved. © 1994 Academic Press Inc.


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