Weak geodesic rays in the space of Kähler potentials and the class E(X,ω)

Abstract

Suppose (X,ω) is a compact Kähler manifold. In the present work we propose a simple construction for weak geodesic rays in the space of Kähler metrics that seems to be tied together with properties of the class E(X,ω). As an application of our construction, we prove a characterization of E(X,ω) in terms of envelopes.

arXiv commentv3. References added. Other minor changes made v4. Final version. Small change in title. Section 2.4 expanded with a result of Ross and Witt-Nystrom on analytic test configurations