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Energy-minimizing
unit vector fields
Yan Digilov, William Eggert, Robert Hardt, James Hart, Michael Jauch, Rob Lewis, Conor Loftis, Aneesh Mehta, Esther Perez, Leobardo Rosales, Anand Shah and Michael Wolf |
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Vol. 3 (2010), No. 4, 435–450
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Abstract |
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Given a surface of revolution with boundary, we study the extrinsic energy of smooth tangent unit-length vector fields. Fixing continuous tangent unit-length vector fields on the boundary of the surface of revolution, we ask if there is a unique smooth tangent unit-length vector field continuously achieving the boundary data and minimizing energy amongst all smooth tangent unit-length vector fields also continuously achieving the boundary data. |
Keywords
calculus of variations, energy, first variation, vector
fields, surfaces of revolution
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Mathematical Subject Classification 2000
Primary: 53A05
Secondary: 49Q99
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Milestones
Received: 27 September 2010
Revised: 12 October 2010
Accepted: 14 October 2010
Published: 6 January 2011
Proposed: Frank Morgan
Communicated by Frank Morgan
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Authors |
| Yan Digilov | |
| Rice University 6100 S. Main Street Houston, TX 77005 United States |
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| William Eggert | |
| Rice University 6100 S. Main Street Houston, TX 77005 United States |
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| Robert Hardt | |
| Department of Mathematics Rice University 6100 S. Main Street MS 136 Houston, TX 77005-1892 United States |
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| James Hart | |
| Rice University 6100 S. Main Street Houston, TX 77005 United States |
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| Michael Jauch | |
| Rice University 6100 S. Main Street Houston, TX 77005 United States |
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| Rob Lewis | |
| Rice University 6100 S. Main Street Houston, TX 77005 United States |
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| Conor Loftis | |
| Rice University 6100 S. Main Street Houston, TX 77005 United States |
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| Aneesh Mehta | |
| Rice University 6100 S. Main Street Houston, TX 77005 United States |
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| Esther Perez | |
| Rice University 6100 S. Main Street Houston, TX 77005 United States |
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| Leobardo Rosales | |
| Department of Mathematics Rice University 6100 S. Main Street MS 136 Houston 77005-1892 United States |
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| Anand Shah | |
| Rice University 6100 S. Main Street Houston, TX 77005 United States |
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| Michael Wolf | |
| Department of Mathematics Rice University 6100 S. Main Street MS 136 Houston 77005-1892 United States |
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| http://math.rice.edu/~mwolf | |
| © 2010 MSP (Mathematical Sciences Publishers). |
