Regularizing properties of Complex Monge-Amp\`ere flows II: Hermitian manifolds
Complex Variables
2020-01-10 v3 Analysis of PDEs
Differential Geometry
Abstract
We prove that a general complex Monge-Amp\`ere flow on a Hermitian manifold can be run from an arbitrary initial condition with zero Lelong number at all points. Using this property, we confirm a conjecture of Tosatti-Weinkove: the Chern-Ricci flow performs a canonical surgical contraction. Finally, we study a generalization of the Chern-Ricci flow on compact Hermitian manifolds, namely the twisted Chern-Ricci flow.
Keywords
Cite
@article{arxiv.1701.04023,
title = {Regularizing properties of Complex Monge-Amp\`ere flows II: Hermitian manifolds},
author = {Tat Dat Tô},
journal= {arXiv preprint arXiv:1701.04023},
year = {2020}
}
Comments
32 pages, final version, to appear in Math. Ann