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Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
University of Massachusetts Amherst
Mathematics and Statistics Department Faculty Publication Series
- Discipline
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
The Spinor Representation Of Minimal Surfaces, Rob Kusner, Nick Schmitt
The Spinor Representation Of Minimal Surfaces, Rob Kusner, Nick Schmitt
Mathematics and Statistics Department Faculty Publication Series
The spinor representation is developed and used to investigate minimal surfaces in R^3 with embedded planar ends. The moduli spaces of planar-ended minimal spheres and real projective planes are determined, and new families of minimal tori and Klein bottles are given. These surfaces compactify in S^3 to yield surfaces critical for the M¨obius invariant squared mean curvature functional W. On the other hand, all Wcritical spheres and real projective planes arise this way. Thus we determine at the same time the moduli spaces of W-critical spheres and real projective planes via the spinor representation.
Dressing Orbits Of Harmonic Maps, Fe Burstall, F Pedit
Dressing Orbits Of Harmonic Maps, Fe Burstall, F Pedit
Mathematics and Statistics Department Faculty Publication Series
We study the harmonic map equations for maps of a Riemann surface into a Riemannian symmetric space of compact type from the point of view of soliton theory. There is a well-known dressing action of a loop group on the space of harmonic maps and we discuss the orbits of this action through particularly simple harmonic maps called {\em vacuum solutions}. We show that all harmonic maps of semisimple finite type (and so most harmonic $2$-tori) lie in such an orbit. Moreover, on each such orbit, we define an infinite-dimensional hierarchy of commuting flows and characterise the harmonic maps of …