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Geodesic distance and Monge-Amp\`ere measures on contact sets

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Abstract

We prove a geodesic distance formula for quasi-psh functions with finite entropy, extending results by Chen and Darvas. We work with big and nef cohomology classes: a key result we establish is the convexity of the $K$-energy in this general setting. We then study Monge-Amp\`ere measures on contact sets, generalizing a recent result by the first author and Trapani.

Dates and versions

hal-03494792 , version 1 (20-12-2021)

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Eleonora Di Nezza, Chinh H. Lu. Geodesic distance and Monge-Amp\`ere measures on contact sets. 2021. ⟨hal-03494792⟩
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