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arXiv · 2107.14117

Ricci curvature, the convexity of volume and minimal Lagrangian submanifolds

Tommaso Pacini
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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.

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Tommaso Pacini. 2021-07-29. Ricci curvature, the convexity of volume and minimal Lagrangian submanifolds. https://arxiv.org/abs/2107.14117

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