Event
Ethan Addison (University of Notre Dame)
Friday, January 14, 2022 11:00to12:00
Title: Generalizing Poincar茅-Type K盲hler Metrics
Abstract: Poincar茅-type metrics are a type of complete cusp metric defined on the complement of a complex hypersurface $X$ in an ambient manifold, yet a result by Auvray shows that constant scalar curvature metrics of Poincar茅-type always split into a product of cscK metrics in each of the ends, inducing a cscK metric on $X$. We prove a result about emph{gnarled} Poincar茅-type metrics using holomorphic flows on $X$ to construct complete cscK metrics near the ends which are perturbations of cscK Poincar茅-type metrics, even when the induced perturbed K盲hler class on $X$ does not admit a cscK metric, thus generalizing the initial flavor of metric to one with fewer restrictions.
听
听
Geometry-Topology
Lieu/Venue: