Session S23 - Group actions in Differential Geometry

Wednesday, July 14, 15:20 ~ 15:50 UTC-3

Minimal 2-spheres in ellipsoids of revolution

Renato Bettiol

CUNY (Lehman College), USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Motivated by Morse-theoretic considerations, Yau asked in 1987 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. 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 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 P. Piccione.

Joint work with Paolo Piccione (Universidade de Sao Paulo, Brazil).

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