Bifurcations of Clifford tori in ellipsoids

Abstract

We prove that 3-dimensional ellipsoids invariant under a 2-torus action contain infinitely many distinct immersed minimal tori, with at most one exception. These minimal tori bifurcate from the 2-torus orbit of largest volume at a dense set of eccentricities, and remain invariant under a circle.

LaTeX2e, 13 pages, 2 figures, final (revised) version. To appear in Math. Res. Lett