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On affine plane curve evolution

Publication ,  Journal Article
Sapiro, G; Tannenbaum, A
Published in: Journal of Functional Analysis
January 1, 1994

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 non-decreasing 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.

Duke Scholars

Published In

Journal of Functional Analysis

DOI

EISSN

1096-0783

ISSN

0022-1236

Publication Date

January 1, 1994

Volume

119

Issue

1

Start / End Page

79 / 120

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics
 

Citation

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ICMJE
MLA
NLM
Sapiro, G., & Tannenbaum, A. (1994). On affine plane curve evolution. Journal of Functional Analysis, 119(1), 79–120. https://doi.org/10.1006/jfan.1994.1004
Sapiro, G., and A. Tannenbaum. “On affine plane curve evolution.” Journal of Functional Analysis 119, no. 1 (January 1, 1994): 79–120. https://doi.org/10.1006/jfan.1994.1004.
Sapiro G, Tannenbaum A. On affine plane curve evolution. Journal of Functional Analysis. 1994 Jan 1;119(1):79–120.
Sapiro, G., and A. Tannenbaum. “On affine plane curve evolution.” Journal of Functional Analysis, vol. 119, no. 1, Jan. 1994, pp. 79–120. Scopus, doi:10.1006/jfan.1994.1004.
Sapiro G, Tannenbaum A. On affine plane curve evolution. Journal of Functional Analysis. 1994 Jan 1;119(1):79–120.
Journal cover image

Published In

Journal of Functional Analysis

DOI

EISSN

1096-0783

ISSN

0022-1236

Publication Date

January 1, 1994

Volume

119

Issue

1

Start / End Page

79 / 120

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics