Minimal spheres in ellipsoids

Início: 26/11/2020 17:00

Término: 26/11/2020 18:00

Palestrante: Paolo Piccione (Universidade de São Paulo)

E-mail do Palestrante:

Resumo: In 1987, Yau posed the question of whether all minimal 2-spheres in a 3-dimensional ellipsoid inside $mathbb{R}^4$ are planar, i.e., determined by the intersection with a hyperplane. While this is the case if the ellipsoid is nearly round, Haslhofer and Ketover have recently shown the existence of an embedded non-planar minimal 2-sphere in sufficiently elongated ellipsoids, with min-max methods. Using bifurcation theory and the symmetries that arise in the case where at least two semi-axes coincide, we show the existence of arbitrarily many distinct embedded non-planar minimal 2-spheres in sufficiently elongated ellipsoids of revolution. This is based on joint work with R. G. Bettiol..