Geometry and Topology Seminar | Jesse Madnick | The Morse index of quartic minimal hypersurfaces

Given a minimal hypersurface S in a round sphere, its Morse index is the number of variations that are area-decreasing to second order. In practice, computing the Morse index of a given minimal hypersurface is extremely difficult, requiring detailed information about the Laplace spectrum of S. Indeed, even for the simplest case in which S is homogeneous, the Morse index of S is not known in general.

In this talk, we compute the Morse index of two such minimal hypersurfaces. Moreover, we observe that their spectra contain both integer eigenvalues as well as (irrational) eigenvalues that are not expressible in radicals. This is joint work with Gavin Ball (Missouri) and Uwe Semmelmann (Stuttgart).

MC 5403