
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
APA
Chicago
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.

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