Metric minimizing surfaces

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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.

Original languageEnglish (US)
Pages (from-to)47-54
Number of pages8
JournalElectronic Research Announcements of the American Mathematical Society
Issue number7
StatePublished - Apr 8 1999

All Science Journal Classification (ASJC) codes

  • General Mathematics


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