January 11, 2022
TITLE: Rigidity of Calabi-Yau metrics with maximal volume growth
ABSTRACT: Calabi-Yau manifolds with maximal volume growth can be seen as 1) higher dimensional generalizations of ALE gravitational instantons and 2) generalizations of asymptotically conical (AC) Calabi-Yau manifolds allowing singular tangent cones at infinity. We first show that on a Calabi-Yau manifold with maximal volume growth, any subquadratic harmonic function must be pluriharmonic. This can be seen as the linearization of the rigidity of the complex Monge-Ampere equation. Next we show that under the additional condition that the metric is ddbar-exact, the metric must be rigid under perturbation by a Kahler potential with subquadratic growth. Part of the talk is joint work in progress with Székelyhidi.