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Bergman Geodesics

Robert Berman (Institutionen för matematiska vetenskaper, matematik) ; Julien Keller
Lecture notes in mathematics (0075-8434). Vol. 2038 (2012), p. 283-302.
[Artikel, refereegranskad vetenskaplig]

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.

Lecture notes in mathematics vol 2038: Complex Monge–Ampère Equations and Geodesics in the Space of Kähler Metrics. Guedj, Vincent (Ed.)

Denna post skapades 2016-05-04.
CPL Pubid: 235910


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Institutionen för matematiska vetenskaper, matematik (2005-2016)



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