Ethan Addison (University of Notre Dame)


Title: Generalizing Poincaré-Type Kähler Metrics

Abstract: Poincaré-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 Poincaré-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} Poincaré-type metrics using holomorphic flows on $X$ to construct complete cscK metrics near the ends which are perturbations of cscK Poincaré-type metrics, even when the induced perturbed Kähler class on $X$ does not admit a cscK metric, thus generalizing the initial flavor of metric to one with fewer restrictions.




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