Kołodziej and Tosatti's conjecture on compact Hermitian manifolds with the bounded mass property

Lei Zhang

Vol. 345 (2026), No. 2, 417–429

DOI: 10.2140/pjm.2026.345.417

Abstract

We prove a conjecture of Kołodziej and Tosatti about Morse-type integrals in nef $(1,1)$ classes on compact Hermitian manifolds with the bounded mass property. Following the original approach of Demailly and Păun, we then extend this result to prove Demailly and Păun’s conjecture in the same setting. Consequently, we obtain a positive answer to a conjecture of Tosatti and Weinkove for compact Hermitian manifolds with the bounded mass property.

Keywords

Monge–Ampère equation, Morse-type integrals, bounded mass property

Mathematical Subject Classification

Primary: 32W20, 53C55

Milestones

Received: 29 March 2026

Revised: 6 June 2026

Accepted: 19 August 2026

Published: 26 October 2026