Seminar

I will talk about a result from a few years ago, which a few other current MSRI members have expressed interest in, concerning the variational properties of natural, conformally invariant functionals on the space of Riemannian metrics. When considered on spheres S^n, such functionals have the remarkable property that the second variation at a critical point (for n > 3) is universal (and positive definite) up to a constant. This means that for several well-known functionals, one can (by computing the particular constants) conclude a local minimum or maximum at the standard round metric on S^n. Examples include: (1) The total Q-curvature, and (2) Regularized spectral invariants, such as the zeta determinant of the Yamabe operator and Dirac operator. This is joint work with Bent Orsted.