Real-analytic geodesics in the Mabuchi space of K\"ahler metrics and quantization
Differential Geometry
2024-01-25 v3
Abstract
We prove the convergence of quantized Bergman geodesics to the Mabuchi geodesics for the initial value problem, in the case of real-analytic initial data and in short time. This partially solves a conjecture of Y. Rubinstein and the last author. We also argue against the existence of a solution to the boundary value problem, generically in real-analytic regularity.
Keywords
Cite
@article{arxiv.2210.00763,
title = {Real-analytic geodesics in the Mabuchi space of K\"ahler metrics and quantization},
author = {Alix Deleporte and Steve Zelditch},
journal= {arXiv preprint arXiv:2210.00763},
year = {2024}
}