Łojasiewicz inequalities for maps of the 2-sphere

Abstract: Infinite-time convergence of geometric flows, as even for finite-dimensional gradient flows, is a notoriously subtle problem. The best (or only) bet is to get a ``Łojasiewicz(-Simon) inequality'' stating that a power of the gradient dominates the distance to the critical energy value. I'll introduce a Łojasiewicz inequality between the tension field and Dirichlet energy of a map from the 2-sphere to itself, removing the technical restrictions from an estimate of Topping (Annals '04). The inequality guarantees convergence of weak solutions of harmonic map flow from $S^2$ to $S^2$ assuming that the body map is nonconstant.

algebraic geometrydifferential geometrysymplectic geometry

Audience: researchers in the topic

Geometria em Lisboa (IST)

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