The Resource A sufficient criterion for a cone to be areaminimizing
A sufficient criterion for a cone to be areaminimizing
Resource Information
The item A sufficient criterion for a cone to be areaminimizing represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item A sufficient criterion for a cone to be areaminimizing represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
 Summary
 One of the fundamental objects of study in geometric measure theory is an "areaminimizing surface." A compact, kdimensional surface (with boundary) is called areaminimizing if no other surface with the same boundary has less surface area. An areaminimizing 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 areaminimizing cone. We present a general method for proving that a cone with an isolated singularity is areaminimizing. 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 areaminimizing. 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 areaminimizing in a small neighborhood of an isolated singularity
 Language
 eng
 Extent
 vi, 111 pages
 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 areaminimizing cones
 Some perturbation results
 Open questions
 Isbn
 9780821825129
 Label
 A sufficient criterion for a cone to be areaminimizing
 Title
 A sufficient criterion for a cone to be areaminimizing
 Language
 eng
 Summary
 One of the fundamental objects of study in geometric measure theory is an "areaminimizing surface." A compact, kdimensional surface (with boundary) is called areaminimizing if no other surface with the same boundary has less surface area. An areaminimizing 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 areaminimizing cone. We present a general method for proving that a cone with an isolated singularity is areaminimizing. 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 areaminimizing. 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 areaminimizing 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 areaminimizing
 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 areaminimizing 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 areaminimizing
 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 areaminimizing 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
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/Asufficientcriterionforaconetobe/ejp59euK1rw/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/Asufficientcriterionforaconetobe/ejp59euK1rw/">A sufficient criterion for a cone to be areaminimizing</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>