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- W2952620753 abstract "Recently the authors showed that there is a robust potential theory attached to any calibrated manifold (X,phi). In particular, on X there exist phi-plurisubharmonic functions, phi-convex domains, phi-convex boundaries, etc., all inter-related and having a number of good properties. In this paper we show that, in a strong sense, the plurisubharmonic functions are the polar duals of the phi-submanifolds, or more generally, the phi-currents studied in the original paper on calibrations. In particular, we establish an analogue of Duval-Sibony Duality which characterizes points in the phi-convex hull of a compact set K in X in terms of phi-positive Green's currents on X and Jensen measures on K. We also characterize boundaries of phi-currents entirely in terms of phi-plurisubharmonic functions. Specific calibrations are used as examples throughout. Analogues of the Hodge Conjecture in calibrated geometry are considered." @default.
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- W2952620753 date "2007-10-21" @default.
- W2952620753 modified "2023-09-27" @default.
- W2952620753 title "Duality of Positive Currents and Plurisubharmonic Functions in Calibrated Geometry" @default.
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