Bergman Geodesics
Journal article, 2012

The aim of this survey is to review the results of Phong-Sturm and Berndtsson on the convergence of Bergman geodesics towards geodesic segments in the space of positively curved metrics on an ample line bundle. As previously shown by Mabuchi, Semmes and Donaldson the latter geodesics may be described as solutions to the Dirichlet problem for a homogeneous complex Monge-Ampere equation. We emphasize in particular the relation between the convergence of the Bergman geodesics and semi-classical asymptotics for Berezin-Toeplitz quantization. Some extension to Wess-Zumino-Witten type equations are also briefly discussed.

Author

Robert Berman

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Julien Keller

CMI Centre de Mathematiques et Informatique

Lecture Notes in Mathematics

0075-8434 (ISSN)

Vol. 2038 283-302

Subject Categories

Mathematics

DOI

10.1007/978-3-642-23669-3_8

ISBN

9783642236686

More information

Created

10/7/2017