The Morse index of quartic minimal hypersurfaces

Abstract: 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. Time permitting, we'll discuss some open problems and work-in-progress. This is joint work with Gavin Ball (Wisconsin) and Uwe Semmelmann (Stuttgart).

differential geometryspectral theory

Audience: researchers in the topic

( paper | video )

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Virtual seminar on geometry with symmetries

Series comments: Description: Research seminar in Lie group actions in Differential geometry.

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