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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

Vol. 3 (2010), No. 4, 435–450
Abstract

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
Mathematical Subject Classification 2000
Primary: 53A05
Secondary: 49Q99
Milestones
Received: 27 September 2010
Revised: 12 October 2010
Accepted: 14 October 2010
Published: 6 January 2011

Proposed: Frank Morgan
Communicated by Frank Morgan
Authors
Yan Digilov
Rice University
6100 S. Main Street
Houston, TX 77005
United States
William Eggert
Rice University
6100 S. Main Street
Houston, TX 77005
United States
Robert Hardt
Department of Mathematics
Rice University
6100 S. Main Street
MS 136
Houston, TX 77005-1892
United States
James Hart
Rice University
6100 S. Main Street
Houston, TX 77005
United States
Michael Jauch
Rice University
6100 S. Main Street
Houston, TX 77005
United States
Rob Lewis
Rice University
6100 S. Main Street
Houston, TX 77005
United States
Conor Loftis
Rice University
6100 S. Main Street
Houston, TX 77005
United States
Aneesh Mehta
Rice University
6100 S. Main Street
Houston, TX 77005
United States
Esther Perez
Rice University
6100 S. Main Street
Houston, TX 77005
United States
Leobardo Rosales
Department of Mathematics
Rice University
6100 S. Main Street
MS 136
Houston 77005-1892
United States
Anand Shah
Rice University
6100 S. Main Street
Houston, TX 77005
United States
Michael Wolf
Department of Mathematics
Rice University
6100 S. Main Street
MS 136
Houston 77005-1892
United States
http://math.rice.edu/~mwolf