Abstract
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–Amp`ere 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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Berman, R., Keller, J. (2012). Bergman Geodesics. In: Guedj, V. (eds) Complex Monge–Ampère Equations and Geodesics in the Space of Kähler Metrics. Lecture Notes in Mathematics(), vol 2038. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23669-3_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-23669-3_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23668-6
Online ISBN: 978-3-642-23669-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)