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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.

Copyright 1999 American Mathematical Society

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Article Info

• ERA Amer. Math. Soc. 05 (1999), pp. 47-54
• Publisher Identifier: S 1079-6762(99)00059-1
• 1991 Mathematics Subject Classification. Primary 53C21
• Key words and phrases.
• Received by the editors September 14, 1998
• Posted on April 8, 1999
• Communicated by Dmitri Burago
• Comments (When Available)

Anton Petrunin

Max-Planck-Institut f\"{u}r Mathematik in den Naturwissenschaften, Inselstrasse 22-26, D-04103 Leipzig, Germany

E-mail address: petrunin@mailhost.mis.mpg.de