English

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}
}