Ricci curvature, the convexity of volume and minimal Lagrangian submanifolds

Abstract

We show that, in toric Kaehler geometry, the sign of the Ricci curvature corresponds exactly to convexity properties of the volume functional. We also discuss analogous relationships in the more general context of quasi-homogeneous manifolds, and existence results for minimal Lagrangian submanifolds.

arXiv comment13 pages. Same results but several improvements and new examples. Supersedes arXiv:2106.14254, thus some overlap. To appear in JSG