Analogues of Zoll surfaces in minimal surface theory

Abstract: About 121 years ago, Otto Zoll described a large family of rotationally symmetric Riemannian two-dimensional spheres whose geodesics are all closed and have the same period. Since then, a very rich (but yet incomplete) theory developed in order to construct and understand geometries (in a broad sense) with these special geodesic flows, also in higher dimensions.

After working on certain systolic questions about minimal two-dimensional spheres in three-dimensional Riemannian spheres with R. Montezuma (UFC), and motivated by other interesting geometric reasons, I became convinced that another sort of higher dimensional generalisation of Zoll surfaces, within the theory of minimal submanifolds, deserved to be investigated on its own. In this talk, we will report on some of the results we proved about these new objects, including existence results, together with F. Codá Marques (Princeton) and A. Neves (UChicago).

differential geometry

Audience: researchers in the topic

B.O.W.L Geometry Seminar