An Introduction to Potential Theory in Calibrated Geometry

Details An Introduction to Potential Theory in Calibrated Geometry An Introduction to Potential Theory in Calibrated Geometry

2007-10-21

arxiv.org/abs/0710.3920v4

Mathematics

Differential Geometry

Minor improvements have been made to the exposition

Scientific paper

We introduce and study the notion of plurisubharmonic functions in calibrated geometry. These functions generalize the classical plurisubharmonic functions from complex geometry and enjoy their important properties. Moreover, they exist in abundance whereas the corresponding pluriharmonics are generally quite scarce. A number of the results established in complex analysis via plurisubharmonic functions are extended to calibrated manifolds. In particular, the notion of pseudo-convexity for a calibrated manifold (X,\phi) is introduced and studied. Analogues of totally real submanifolds are also introduced and used to construct enormous families of strictly \phi-convex spaces with every topological type allowed by Morse Theory. Specific calibrations are used as examples throughout.

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