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Metric minimizing surfaces
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## Metric minimizing surfaces

### Anton Petrunin

**Abstract.**
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`

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