Weak geodesic rays in the space of K\"ahler potentials and the class E(X,\omega)

TL;DR

This paper introduces a new method for constructing weak geodesic rays in the space of Kähler metrics on compact manifolds, linking these constructions to the properties of the class E(X,ω) and providing a characterization via envelopes.

Contribution

It presents a simple construction for weak geodesic rays tied to the class E(X,ω), offering new insights into their structure and properties.

Findings

Construction of weak geodesic rays in Kähler metric space

Characterization of E(X,ω) via envelopes

Link between geodesic rays and class E(X,ω) properties

Abstract

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