English

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 KK-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