November 19, 2021
Minimal 2-spheres in ellipsoids of revolution
Motivated by Morse-theoretic considerations, Yau asked in 1987 whether all minimal 2-spheres in a 3-dimensional ellipsoid inside R^4 are planar, i.e., determined by the intersection with a hyperplane. Recently, this was shown not to be the case by Haslhofer and Ketover, who produced an embedded non-planar minimal 2-sphere in sufficiently elongated ellipsoids, combining Mean Curvature Flow and Min-Max methods. Using Bifurcation Theory and the symmetries that arise if at least two semiaxes 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 P. Piccione.