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The Resource A sufficient criterion for a cone to be area-minimizing

A sufficient criterion for a cone to be area-minimizing

Label
A sufficient criterion for a cone to be area-minimizing
Title
A sufficient criterion for a cone to be area-minimizing
Creator
Subject
Language
eng
Summary
One of the fundamental objects of study in geometric measure theory is an "area-minimizing surface." A compact, k-dimensional surface (with boundary) is called area-minimizing if no other surface with the same boundary has less surface area. An area-minimizing surface can have singularities. The main purpose of this paper is to investigate some of the shapes that such singularities can have. A key concept in this study is that of an area-minimizing cone. We present a general method for proving that a cone with an isolated singularity is area-minimizing. The calculation involves the curvature (second fundamental form) and a sort of "embedding radius" of the normal bundle to the cone. We can also prove that certain cones are not area-minimizing. Using this method, we complete the classification of minimizing cones over products of spheres. We also give other examples, including the first known unorientable minimizing cones. The method also lends itself to perturbation arguments. We show that certain surfaces are area-minimizing in a small neighborhood of an isolated singularity
Cataloging source
UkLiU
http://library.link/vocab/creatorDate
1961-
http://library.link/vocab/creatorName
Lawlor, Gary R.
Series statement
Memoirs of the American Mathematical Society
Series volume
446
http://library.link/vocab/subjectName
  • Geometric measure theory
  • Cone
Label
A sufficient criterion for a cone to be area-minimizing
Instantiates
Publication
Bibliography note
Includes bibliographical references (page 111)
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Appendix
  • Introduction
  • A minimization test for cones
  • Calibrations
  • The differential equation
  • Cones for which the criterion is necessary as well as sufficient
  • Examples of area-minimizing cones
  • Some perturbation results
  • Open questions
Dimensions
26 cm.
Extent
vi, 111 pages
Isbn
9780821825129
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
Label
A sufficient criterion for a cone to be area-minimizing
Publication
Bibliography note
Includes bibliographical references (page 111)
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Appendix
  • Introduction
  • A minimization test for cones
  • Calibrations
  • The differential equation
  • Cones for which the criterion is necessary as well as sufficient
  • Examples of area-minimizing cones
  • Some perturbation results
  • Open questions
Dimensions
26 cm.
Extent
vi, 111 pages
Isbn
9780821825129
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations

Library Locations

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      Ashton Street, Liverpool, L69 3DA, GB
      53.418074 -2.967913
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