Pure and Applied Mathematics Quarterly

Volume 17 (2021)

Number 3

Special Issue in Honor of Duong H. Phong

Edited by Tristan Collins, Valentino Tosatti, and Ben Weinkove

Morse-type integrals on non-Kähler manifolds

Pages: 991 – 1004

DOI: https://dx.doi.org/10.4310/PAMQ.2021.v17.n3.a6


Sławomir Kołodziej (Faculty of Mathematics and Computer Science, Jagiellonian University, 30-348 Kraków, Poland)

Valentino Tosatti (Department of Mathematics and Statistics, McGill University, Montréal, Québec, Canada; and Department of Mathematics, Northwestern University, Evanston Illinois, U.S.A.)


We pose a conjecture about Morse-type integrals in nef $(1,1)$ classes on compact Hermitian manifolds, and we show that it holds for semipositive classes, or when the manifold admits certain special Hermitian metrics.

The first-named author was partially supported by NCN grant 2017/27/B/ST1/01145.

The second-named author was partially supported by NSF grants DMS-1610278 and DMS-1903147.

Received 3 May 2019

Accepted 23 June 2019

Published 14 June 2021