Metric minimizing surfaces

Anton Petrunin

doi:10.1090/S1079-6762-99-00059-1

Metric minimizing surfaces

Anton Petrunin

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

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.

Original language	English (US)
Pages (from-to)	47-54
Number of pages	8
Journal	Electronic Research Announcements of the American Mathematical Society
Volume	5
Issue number	7
DOIs	https://doi.org/10.1090/S1079-6762-99-00059-1
State	Published - Apr 8 1999

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1090/S1079-6762-99-00059-1

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title = "Metric minimizing surfaces",

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.",

author = "Anton Petrunin",

year = "1999",

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doi = "10.1090/S1079-6762-99-00059-1",

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Y1 - 1999/4/8

N2 - 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.

AB - 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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U2 - 10.1090/S1079-6762-99-00059-1

DO - 10.1090/S1079-6762-99-00059-1

M3 - Article

AN - SCOPUS:85009787605

SN - 1079-6762

VL - 5

SP - 47

EP - 54

JO - Electronic Research Announcements of the American Mathematical Society

JF - Electronic Research Announcements of the American Mathematical Society

IS - 7

ER -

Metric minimizing surfaces

Abstract

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