Publication Cover
Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 2
53
Views
1
CrossRef citations to date
0
Altmetric
Articles

Plane R-curves II

, &
Pages 275-289 | Received 11 May 2018, Accepted 20 Mar 2019, Published online: 03 Apr 2019

References

  • Longinetti M, Manselli P, Venturi A. Plane R-curves and their steepest descent properties I. Appl Anal. DOI: 10.1080/00036811.2018.1466278.
  • Manselli P, Pucci C. Maximum length of steepest descent curves for quasi-convex functions. Geom Ded. 1991;38:211–227. doi: 10.1007/BF00181220
  • Mainik IF. An estimate of the length of the curves of descent. Sibirsk Mat Zh. 1992;33:215–218.
  • Daniilidis A, Ley O, Sabourau S. Asymptotic behaviour of self-contracting planar curves and gradient orbits of convex functions. J Math Pures Appl. 2010;94:183–199. doi: 10.1016/j.matpur.2010.03.007
  • Longinetti M, Manselli P, Venturi A. On steepest descent curves for quasi-convex families in Rn. Math Nachr. 2015;288:420–442. doi: 10.1002/mana.201300133
  • Daniilidis A, David G, Durand-Cartagena E, et al. Rectifiability of self-contracted curves in the Euclidean space and applications. J Geom Anal. 2015;25:1211–1239. doi: 10.1007/s12220-013-9464-z
  • Lemenant A. Rectifiability of non-Euclidean planar self-contracted curves. Confluentes Math. 2016;8:23–38. doi: 10.5802/cml.31
  • Daniilidis A, Deville R, Durand-Cartagena E, et al. Self-contracted curves in Riemannian manifolds. J Math Anal Appl. 2018;457:1333–1352. doi: 10.1016/j.jmaa.2017.04.011
  • Stepanov E, Teplitskaya Y. Self-contracted curves have finite length. J London Math Soc. 2017;96:455–481. doi: 10.1112/jlms.12068
  • Aichholzer O, Aurenhammer F, Icking C, et al. Generalized self-approaching curves. Discr Appl Math. 2001;109:3–24. doi: 10.1016/S0166-218X(00)00233-X
  • Daniilidis A, Deville R, Durand-Cartagena E. Metric and geometric relaxation of self-contracted curves. J Optim Theory Appl. DOI: 10.1007/s10957-018-1408-0.
  • Ohta S. Self-contracted curves in CAT(0)-spaces and their rectifiability. J Geom Anal. 2019. DOI:10.1007/s12220-018-00126-7.
  • Federer H. Curvature measure. Trans Am Math Soc. 1959;93:418–481. doi: 10.1090/S0002-9947-1959-0110078-1
  • Colesanti A, Manselli P. Geometric and isoperimetric properties of sets of positive reach in Ed. Atti Semin Mat Fis Univ Modena Reggio Emilia. 2010;57:97–113.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.