Energy-minimizing unit vector fields
Yan Digilov, William Eggert, Robert Hardt, James Hart, Michael Jauch, Rob Lewis, Conor Loftis, Aneesh Mehta, Hector Perez, Leobardo Rosales, Anand Shah, Michael Wolf · Involve a Journal of Mathematics · 2010
Given a surface of revolution with boundary, we study the extrinsic energy of smooth tangent unit-length vector fields.Fixing continuous tangent unitlength 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.