Complex Brunn-Minkowski theory - Bo Berndtsson
Channel: UMD Mathematics
Date: 19/11/2018

Complex Brunn-Minkowski theory
Friday, November 2, at 3:15pm
Bo Berndtsson
Location: Kirwan Hall 3206

Abstract: In the second lecture we will turn to applications. In the first application we will give a proof of a sharp version of a famous result in complex analysis on extension with L^2-estimates of holomorphic functions defined on subvarieties of a pseudoconvex domain, the Ohsawa-Takegoshi theorem. In the proof we deform the ambient domain to a trivial case and use our theorem to show monotonicity of the constants under the deformation (joint work with L. Lempert). The next application is to the Mabuchi space of positively curved metrics on a fixed line bundle over a compact complex manifold. We will sketch a proof of a generalization of the Bando-Mabuchi uniqueness theorem for Kahler-Einstein metrics, using a complex version of Prekopa's theorem. Finally, we shall discuss applications to some positivity results from algebraic geometry, starting with a classical theorem of Griffiths.