Skip to main content
Article thumbnail
Location of Repository

Duality of positive currents and plurisubharmonic functions in calibrated geometry

By F. Reese Harvey and H. Blaine Lawson

Abstract

Recently the authors showed that there is a robust potential theory attached to any calibrated manifold (X, φ). In particular, on X there exist φ-plurisubharmonic functions, φ-convex domains, φ-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 φ-submanifolds, or more generally, the φ-currents studied in the original paper on calibrations. In particular, we establish an analogue of Duval-Sibony Duality which characterizes points in the φ-convex hull of a compact set K ⊂ X in terms of φ-positive Green’s currents on X and Jensen measures on K. We also characterize boundaries of φ-currents entirely in terms of φ-plurisubharmonic functions. Specific calibrations are used as examples throughout. Analogues of the Hodge Conjecture in calibrated geometry are considered

Topics: TABLE OF CONTENTS
Year: 2009
OAI identifier: oai:CiteSeerX.psu:10.1.1.135.2344
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • http://arxiv.org/pdf/0710.3921... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.