# Flowing to minimal surfaces

#### Melanie Rupflin, University of Oxford. Part of geometry seminar series.

For maps from surfaces there is a close connection between the area functional and Dirichlet energy and thus also between their critical points. As such, one way to try to find minimal surfaces is to consider a gradient flow of the Dirichlet energy, which not only evolves a map but also the domain metric in order to find a map that is not only harmonic but also (weakly) conformal and thus a (branched) minimal immersion. In this talk I will discuss the construction of such a flow, the Teichmueller harmonic map flow, and explain in particular how this flow decomposes any given initial map from a closed surface into minimal surfaces. This is joint work with Peter Topping.

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