The Resource A sufficient criterion for a cone to be area-minimizing
A sufficient criterion for a cone to be area-minimizing
Resource Information
The item A sufficient criterion for a cone to be area-minimizing 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 area-minimizing 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 "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
- 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 area-minimizing cones
- Some perturbation results
- Open questions
- Isbn
- 9780821825129
- Label
- A sufficient criterion for a cone to be area-minimizing
- Title
- A sufficient criterion for a cone to be area-minimizing
- 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
- 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
- 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
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/A-sufficient-criterion-for-a-cone-to-be/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/A-sufficient-criterion-for-a-cone-to-be/ejp59euK1rw/">A sufficient criterion for a cone to be area-minimizing</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>
