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

[1] Maclane, Saunders, Schilling, O. F. G. Infinite number fields with Noether ideal theories Amer. J. Math. 1939 771 782

[2] Gromov, Mikhael Structures métriques pour les variétés riemanniennes 1981

[3] Nikolaev, Igor The tangent cone of an Aleksandrov space of curvature ≤𝐾 Manuscripta Math. 1995 137 147

[4] Petrunin, A. Parallel transportation for Alexandrov space with curvature bounded below Geom. Funct. Anal. 1998 123 148

[5] Reå¡Etnjak, Ju. G. Non-expansive maps in a space of curvature no greater than 𝐾 Sibirsk. Mat. Ž. 1968 918 927

[6] Å Arafutdinov, V. A. Radius of injectivity of a complete open manifold of nonnegative curvature Dokl. Akad. Nauk SSSR 1976 46 48

[7] ŠEfel′, S. Z. On saddle surfaces bounded by a rectifiable curve Dokl. Akad. Nauk SSSR 1965 294 296

[8] ŠEfel′, S. Z. On the intrinsic geometry of saddle surfaces Sibirsk. Mat. Ž. 1964 1382 1396

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