Zoll-like metrics in minimal surface theory

Início: 19/08/2022 17:00

Término: 19/08/2022 18:00

Palestrante: Lucas Ambrozio (IMPA)

E-mail do Palestrante: l.ambrozio@impa.br

Resumo: a Zoll metric is a Riemannian metric g on a manifold such that all of its geodesics are periodic and have the same finite fundamental period. In particular, (M,g) is a compact manifold such that each tangent one-dimensional subspace of each one of its points is tangent to some closed geodesic. Since periodic geodesics are not only periodic orbits of a flow, but also closed curves that are critical points of the length functional, the notion of Zoll metrics admits natural generalisations in the context of minimal submanifold theory, that is, the theory of critical points of the area functional. In this talk, based on joint work with F. Codá (Princeton) and A. Neves (UChicago), I will discuss why these new, generalised notions seem relevant to me beyond its obvious geometric appeal, and discuss two different methods to obtain infinitely many such examples on spheres, with perhaps unexpected properties.