Publicación: Metric and Geometric Relaxations of Self-Contracted Curves
Fecha
2018-10-13
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info:eu-repo/semantics/openAccess
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Springer Nature
Resumen
The metric notion of a self-contracted curve (respectively, self-expanded curve, if we reverse the orientation) is hereby extended in a natural way. Two new classes of curves arise from this extension, both depending on a parameter, a specific value of which corresponds to the class of self-expanded curves. The first class is obtained via a straightforward metric generalization of the metric inequality that defines self-expandedness, while the second one is based on the (weaker) geometric notion of the so-called cone property (eel-curve). In this work, we show that these two classes are different; in particular, curves from these two classes may have different asymptotic behavior. We also study rectifiability of these curves in the Euclidean space, with emphasis in the planar case.
Descripción
The registered version of this article, first published in Journal of Optimization Theory and Applications, is available online at the publisher's website: Springer Nature, https://doi.org/10.1007/s10957-018-1408-0
La versión registrada de este artículo, publicado por primera vez en Journal of Optimization Theory and Applications, está disponible en línea en el sitio web del editor: Springer Nature, https://doi.org/10.1007/s10957-018-1408-0
La versión registrada de este artículo, publicado por primera vez en Journal of Optimization Theory and Applications, está disponible en línea en el sitio web del editor: Springer Nature, https://doi.org/10.1007/s10957-018-1408-0
Categorías UNESCO
Palabras clave
self-contracted curve, self-expanded curve, rectifiability, length, λ-curve, λ-cone property
Citación
Daniilidis, A., Deville, R. & Durand-Cartagena, E. Metric and Geometric Relaxations of Self-Contracted Curves. J Optim Theory Appl 182, 81–109 (2019). https://doi.org/10.1007/s10957-018-1408-0
Centro
Facultades y escuelas::E.T.S. de Ingenieros Industriales
Departamento
Matemática Aplicada I