Length of curves on Lip manifolds

Giuseppe De Cecco; Giuliana Palmieri

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1990)

  • Volume: 1, Issue: 3, page 215-221
  • ISSN: 1120-6330

Abstract

top
In this paper the length of a curve on a Lipschitz Riemannian manifold is defined. It is shown that the above definition is consistent with the definition of the geodesic distance already introduced by the authors, both in a geometrical and analytical way.

How to cite

top

De Cecco, Giuseppe, and Palmieri, Giuliana. "Length of curves on Lip manifolds." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 1.3 (1990): 215-221. <http://eudml.org/doc/244275>.

@article{DeCecco1990,
abstract = {In this paper the length of a curve on a Lipschitz Riemannian manifold is defined. It is shown that the above definition is consistent with the definition of the geodesic distance already introduced by the authors, both in a geometrical and analytical way.},
author = {De Cecco, Giuseppe, Palmieri, Giuliana},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Lipschitz manifold; Length; Nonsmooth analysis; Lipschitz manifolds; geodesic distance; Lipschitz curves},
language = {eng},
month = {9},
number = {3},
pages = {215-221},
publisher = {Accademia Nazionale dei Lincei},
title = {Length of curves on Lip manifolds},
url = {http://eudml.org/doc/244275},
volume = {1},
year = {1990},
}

TY - JOUR
AU - De Cecco, Giuseppe
AU - Palmieri, Giuliana
TI - Length of curves on Lip manifolds
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1990/9//
PB - Accademia Nazionale dei Lincei
VL - 1
IS - 3
SP - 215
EP - 221
AB - In this paper the length of a curve on a Lipschitz Riemannian manifold is defined. It is shown that the above definition is consistent with the definition of the geodesic distance already introduced by the authors, both in a geometrical and analytical way.
LA - eng
KW - Lipschitz manifold; Length; Nonsmooth analysis; Lipschitz manifolds; geodesic distance; Lipschitz curves
UR - http://eudml.org/doc/244275
ER -

References

top
  1. DE CECCO, G. - PALMIERI, G., Distanza intrinseca su una varietà riemanniana di Lipschitz. Rend. Sem. Mat. Torino, to appear. 
  2. DE CECCO, G. - PALMIERI, G., Integral distance on a Lipschitz Riemannian manifold. Rapporti Dip. Mat. Un. Bari, n. 2, 1990. Zbl0722.58006
  3. DE GIORGI, E., Su alcuni problemi comuni all'Analisi e alla Geometria. Atti Conv. Geom. Diff. Lecce, Note di Matematica, 9, (Supplemento), 1989, to appear. 
  4. GROMOV, M. (rédigé par J. Lafontaine, P. Pansu), Structures métriques pour les variétés riemanniennes. Cedic-Nathan, Paris1981. Zbl0509.53034MR682063
  5. LUUKKAINEN, J. - VÄISÄLÄ, J., Elements of Lipschitz Topology. Ann. Ac. Sc. Fennicae, 3, 1977. Zbl0397.57011MR515647
  6. RINOW, W., Die innere Geometrie der metrischen Räume. Springer, 1961. Zbl0096.16302MR123969
  7. TELEMAN, N., The Index of Signature Operators on Lipschitz Manifolds. Publ. Math. IHES, 58, 1983, 261-290. Zbl0531.58044MR720931
  8. WHITNEY, H., Geometric Integration Theory. Princeton Univ. Press, 1956. Zbl0083.28204MR87148

NotesEmbed ?

top

You must be logged in to post comments.