Generalized K\"ahler-Ricci flow on toric Fano varieties
Differential Geometry
2022-01-07 v2 Analysis of PDEs
Abstract
We study the generalized K\"ahler-Ricci flow with initial data of symplectic type, and show that this condition is preserved. In the case of a Fano background with toric symmetry, we establish global existence of the normalized flow. We derive an extension of Perelman's entropy functional to this setting, which yields convergence of nonsingular solutions at infinity. Furthermore, we derive an extension of Mabuchi's -energy to this setting, which yields weak convergence of the flow.
Keywords
Cite
@article{arxiv.2104.03268,
title = {Generalized K\"ahler-Ricci flow on toric Fano varieties},
author = {Vestislav Apostolov and Jeffrey Streets and Yury Ustinovskiy},
journal= {arXiv preprint arXiv:2104.03268},
year = {2022}
}
Comments
Final version to appear Trans. AMS. Significantly condensed from V1