Let X be a compact complex manifold of complex dimension n and α be a smooth closed real form on X such that its cohomology class {α}∈H1,1(X,R) is big. In this paper we prove that, given a bounded function f with bounded distributional laplacian in X, the α-psh envelope P(f) is also locally bounded with locally bounded distributional laplacian on the ample locus of {α}.
Di Nezza, E., Trapani, S. (2024). Regularity of Envelopes. ANNALES SCIENTIFIQUES DE L'ECOLE NORMALE SUPERIEURE, tomo 57 serie 4(5), 1347-1370 [10.24033/asens.2592].
Regularity of Envelopes
Di Nezza, E;
2024-09-01
Abstract
Let X be a compact complex manifold of complex dimension n and α be a smooth closed real form on X such that its cohomology class {α}∈H1,1(X,R) is big. In this paper we prove that, given a bounded function f with bounded distributional laplacian in X, the α-psh envelope P(f) is also locally bounded with locally bounded distributional laplacian on the ample locus of {α}.File in questo prodotto:
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