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Geometric Analysis: Rigidity of conformally invariant functionals April 07, 2016 (11:00 AM PDT - 12:00 PM PDT)
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Location: MSRI: Simons Auditorium
Speaker(s) Niels Moeller (Abdus Salam International Centre for Theoretical Physics)
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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.

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