Noncommutative potential theory
Complex Variables
2016-10-13 v1 Functional Analysis
Abstract
We propose to view hermitian metrics on trivial holomorphic vector bundles as noncommutative analogs of functions defined on the base , and curvature as the notion corresponding to the Laplace operator or . We discuss noncommutative generalizations of basic results of ordinary potential theory, mean value properties, maximum principle, Harnack inequality, and the solvability of Dirichlet problems.
Cite
@article{arxiv.1610.03523,
title = {Noncommutative potential theory},
author = {Laszlo Lempert},
journal= {arXiv preprint arXiv:1610.03523},
year = {2016}
}