Geodesic
Metric minimizing surfaces
Petrunin, Anton1
1 Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstrasse 22-26, D-04103 Leipzig, Germany
Electronic research announcements of the American Mathematical Society, Tome 05 (1999), pp. 47-54.

Voir la notice de l'article provenant de la source American Mathematical Society

Consider a two-dimensional surface in an Alexandrov space of curvature bounded above by $k$. Assume that this surface does not admit contracting deformations (a particular case of such surfaces is formed by area minimizing surfaces). Then this surface inherits the upper curvature bound, that is, this surface has also curvature bounded above by $k$, with respect to the intrinsic metric induced from its ambient space.
DOI : 10.1090/S1079-6762-99-00059-1

Petrunin, Anton 1

1 Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstrasse 22-26, D-04103 Leipzig, Germany 
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Petrunin, Anton. Metric minimizing surfaces. Electronic research announcements of the American Mathematical Society, Tome 05 (1999), pp. 47-54. doi : 10.1090/S1079-6762-99-00059-1. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-99-00059-1/

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