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Blaine Lawson: Lectures

September 2016 – LECTURE CANCELLED
TITLE: Pluripotential theory on calibrated manifolds

ABSTRACT: A calibrated manifold (X, \phi) carries a geometry of distinguished \phi-submanifolds and \phi-currents. This is relatively well-known. However, X, \phi also carries distinguished analytic objects: the \phi-plurisubharmonic functions, which are, in a sense, dual to the currents. Somewhat surprisingly much of the classical pluripotential theory in several complex variables extends to the context of calibrations. This includes d d^\phi-operators, notions of convexity, maximal functions (the analogues of solutions to the complex Monge-Ampère equation), and solving the Dirichlet Problem for such functions. I will discuss what is known in this area, and pose a number of questions and problems.

Slides prepared for lecture