English

Degenerate J-flow on compact K\"ahler manifolds

Differential Geometry 2023-03-07 v3 Analysis of PDEs Complex Variables

Abstract

In this note, we study a degenerate twisted J-flow on compact K\"ahler manifolds. We show that it exists for all time, it is unique and converges to a weak solution of a degenerate twisted J-equation. In particular, this confirms an expectation formulated by Song-Weinkove for the J-flow. As a consequence, we establish the properness of the Mabuchi K-energy twisted by a certain semi-positive closed (1,1)-form for K\"ahler classes in a certain subcone.

Keywords

Cite

@article{arxiv.2201.09380,
  title  = {Degenerate J-flow on compact K\"ahler manifolds},
  author = {Tat Dat Tô},
  journal= {arXiv preprint arXiv:2201.09380},
  year   = {2023}
}

Comments

Lemma 3.7 corrected, final version, to appear in Math. Z