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Metric minimizing surfaces

Author: Anton Petrunin
Journal: Electron. Res. Announc. Amer. Math. Soc. 5 (1999), 47-54
MSC (1991): Primary 53C21
Published electronically: April 8, 1999
MathSciNet review: 1679453
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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.

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Additional Information

Anton Petrunin
Affiliation: Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstrasse 22-26, D-04103 Leipzig, Germany

Received by editor(s): September 14, 1998
Published electronically: April 8, 1999
Additional Notes: The main part of this note was prepared when the author had a postdoctoral fellowship at MSRI (Berkeley).
Communicated by: Dmitri Burago
Article copyright: © Copyright 1999 American Mathematical Society