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University of Regina Department of Mathematics and Statistics

University of Regina
Department of Mathematics and Statistics
Speaker: Peter Quast (University of Augsburg, Germany)
Title: Generalizing surfaces of constant mean curvature
Date: Friday, March 7, 2008
Time: 3:30
Place: Math & Stats Lounge (CW 307.20)
The Gauss map of a (parameterized) surface assigns to each point the
unit normal vector, which is an element of the 2-sphere. One may ask how
geometric properties of a surface are encoded in its Gauss map. An example
is the famous theorem of Ruh and Vilms. It states that a conformally
parameterized surface has constant mean curvature (CMC) if and only if its
Gauss map is harmonic (i.e. a critical point of the energy functional). On the
other hand given a harmonic map into the 2-sphere one can (under suitable
assumptions) construct a pair of conformal CMC-surfaces whose Gauss map
is the given harmonic map. This construction goes back to Bonnet in the
19th century. At the beginning of the 1990s Bobenko gave a more explicit
and geometric way to recover CMC surfaces from their harmonic Gauss


Source: Argerami, Martin - Department of Mathematics and Statistics, University of Regina


Collections: Mathematics