Anna Siffert

A new structural approach to isoparametric hypersurfaces in spheres

In this paper we show that the long-standing problem of classifying all isoparametric hypersurfaces in spheres with six different principal curvatures is still not complete. Moreover, we develop a structural approach that may be helpful for such a classification. Instead of working with the isoparametric hypersurface family in the sphere, we consider the associated Lagrangian submanifold of the real Grassmannian of oriented 2-planes in

Harmonic self-maps of cohomogeneity one manifolds

{\mathbb {R}}^{n+2}

The systole of large genus minimal surfaces in positive Ricci curvature.

Rn+2. We obtain new geometric insights into classical invariants and identities in terms of the geometry of the Lagrangian submanifold.