A complete metric topology on relative low energy spaces

Abstract

In this paper, we show that the low energy spaces in the prescribed singularity case ${\mathcal{E}}_{\psi }(X,\theta ,\varphi )$ have a natural topology which is completely metrizable. This topology is stronger than convergence in capacity.

25 pages, comments are welcome

References in corpus (1)

• To the geometry of spaces of plurisubharmonic functions on a Kähler manifold

Cited by in corpus (2)

• Entropy for Monge-Ampère Measures in the Prescribed Singularities Setting
• Relative pluripotential theory on compact Kähler manifolds