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

Eleonora Di Nezza (1, 2) , Chinh H. Lu (3)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 SU - Sorbonne Université
3 LMO - Laboratoire de Mathématiques d'Orsay

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.

Domains: Complex Variables [math.CV]; Differential Geometry [math.DG]

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