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

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.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal-universite-paris-saclay.archives-ouvertes.fr/hal-03494792
Contributor : Hoang-Chinh Lu Connect in order to contact the contributor
Submitted on : Monday, December 20, 2021 - 7:41:51 AM
Last modification on : Tuesday, January 4, 2022 - 5:47:32 AM

### Identifiers

• HAL Id : hal-03494792, version 1
• ARXIV : 2112.09627

### Citation

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

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