The Regularity of Envelopes

Abstract

Let $X$ be a compact complex manifold of complex dimension $n$ and $\alpha$ be a smooth closed real form on $X$ such that its cohomology class $\{\alpha \}\in H^{1,1}(X,\mathbb{R})$ is big. In this paper we prove that, given a bounded function $f$ with bounded distributional laplacian in $X,$ the $\alpha$-psh envelope $P(f)$ is also locally bounded with locally bounded distributional laplacian on the ample locus of $\{\alpha \}.$

20 pages

References in corpus (1)

• On the singularity type of full mass currents in big cohomology classes