Demailly, Jean-Pierre Pseudoconvex-concave duality and regularization of currents. (English) Zbl 0960.32011 Schneider, Michael (ed.) et al., Several complex variables. Cambridge: Cambridge University Press. Math. Sci. Res. Inst. Publ. 37, 233-271 (1999). The paper investigates some basic properties of Finsler metrics on holomorphic vector bundles in the perspective of obtaining geometric versions of the Serre duality theorem. A duality framework under which pseudo-convexity and pseudo-concavity properties get exchanged is established. These duality properties are related to several geometric problems, e.g., the conjecture of Hartshorne and Schneider.Finally, a new shorter and more geometric proof of a basic regularization theorem for closed \((1,1)\)-currents is shown.For the entire collection see [Zbl 0933.00014]. Reviewer: Viorel Vâjâitu (Bucureşti) Cited in 8 Documents MSC: 32F10 \(q\)-convexity, \(q\)-concavity 32C30 Integration on analytic sets and spaces, currents 32J25 Transcendental methods of algebraic geometry (complex-analytic aspects) Keywords:Hartshorne-Schneider conjecture; plurisubharmonic function; regularization of currents; Finsler metrics; pseudoconvexity; pseudoconcavity PDF BibTeX XML Cite \textit{J.-P. Demailly}, Math. Sci. Res. Inst. Publ. 37, 233--271 (1999; Zbl 0960.32011) Full Text: Link OpenURL