Pluri-subharmonic functions on complex tori, Ricci curvature and convexity
arXiv:2106.14254
Abstract
We show that, in toric manifolds, one can characterize the sign of the Ricci curvature in terms of the convexity of the volume functional. More generally we discuss relationships between (i) Ricci curvature and volume, (ii) totally real and Lagrangian submanifolds, (iii) pluri-subharmonic functions and convexity.
First draft version, part of a larger research project. Comments welcome