Rigidity of $\epsilon$-harmonic maps of low degree

Abstract: In 1981 Sacks and Uhlenbeck introduced their famous alpha-approximation of the Dirichlet energy for maps from surfaces and showed that critical points converge (away from finitely many points) to a harmonic map. Now one can ask whether every harmonic map is captured by this limiting process. Lamm, Malchiodi and Micallef answered this for maps from the two sphere into the two sphere and showed that the Sacks-Uhlenbeck method produces only constant maps and rotations if the energy lies below a certain threshold. We investigate the same question for the epsilon-approximation of the Dirichlet energy. Joint work with Tobias Lamm and Mario Micallef.

Computer scienceanalysis of PDEsdifferential geometrymetric geometry

Audience: researchers in the topic

Online Seminar "Geometric Analysis"

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