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Acta Mathematica Vietnamica

Lp Metric Geometry of Big and Nef Cohomology Classes

Eleonora Di Nezza , icon-email Chinh H. Lu

Abstract

Let (X,ω) be a compact Kähler manifold of dimension n, and let θ be a closed smooth real (1,1)-form representing a big and nef cohomology class. We introduce a metric dp, p1, on the finite energy space Ep(X,θ), making it a complete geodesic metric space.