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

Concave elliptic equations and generalized Khovanskii–Teissier inequalities

Pages: 1061 – 1082

DOI: https://dx.doi.org/10.4310/PAMQ.2021.v17.n3.a10


Tristan C. Collins (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A.)


We explain a general construction through which concave elliptic operators on complex manifolds give rise to concave functions on cohomology. In particular, this leads to generalized versions of the Khovanskii–Teissier inequalities.

2010 Mathematics Subject Classification

Primary 32J25. Secondary 32J18.

The author is supported in part by NSF grant DMS-1810924, and by an Alfred P. Sloan Fellowship.

Received 18 March 2019

Accepted 23 July 2019

Published 14 June 2021