Department of Mathematics

PhD Anda Degeratu (Universität Freiburg): "The calabi conjecture on QAC spaces"

Jul 02, 2015 from 04:15 PM to 05:15 PM

LMS 4 - Raum 526 - Übungsraum


In this talk I will introduce the class of quasi-asymptotically conical (QAC) manifolds, a less rigid Riemannian formulation of the QALE geometries introduced by Joyce in his study of crepant resolutions of Calabi-Yau orbifolds. Our set-up is in the category of real stratified spaces and Riemannian geometry. Given a QAC manifold, we identify the appropriate weighted Sobolev spaces, for which we prove the finite dimensionality of the null space for generalized Laplacian as well as their Fredholmness. We then use this to prove existence and uniqueness of solutions to Monge-Ampere equation.

The methods we use are based on techniques developed in geometric analysis by Grigor'yan and Saloff-Coste,  as well as Colding and Minicozzi, and Peter Li. We show that our geometries satisfy the volume doubling property and the Poincaré inequality, and we use these properties to analyze the heat kernel behaviour of a generalized Laplacian and to establish Li-Yau type estimates for it.

This work is joint with Rafe Mazzeo.

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