Global solutions of the Teichmueller harmonic map flow
Geometric Flows in Riemannian and Complex Geometry May 02, 2016 - May 06, 2016
Location: SLMath: Eisenbud Auditorium
harmonic maps
Riemannian geometry
complex geometry
geometric analysis
geometric flow
Ricci flow
diffeomorphism groups
singularities of flows
51D25 - Lattices of subspaces and geometric closure systems [See also 05B35]
51D30 - Continuous geometries, geometric closure systems and related topics [See also 06Cxx]
28C15 - Set functions and measures on topological spaces (regularity of measures, etc.)
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The Teichmueller harmonic map flow is a gradient flow of the classical harmonic map energy, in which both a map from a surface and the metric on that surface are allowed to evolve. In principle, the flow wants to find minimal immersions. However, in general, the domain metric might degenerate in finite time. In this talk we show how to flow beyond finite time singularities, and this allows us to decompose a general map into a collection of minimal immersions.
This is forthcoming work joint with Melanie Rupflin
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