Degenerate J-flow on compact Kähler manifolds

Abstract

In this note, we study a degenerate twisted J-flow on compact Kähler 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 Kähler classes in a certain subcone.

arXiv commentLemma 3.7 corrected, final version, to appear in Math. Z