2016/10/11 by Laszlo Lempert, Lempert, Laszlo
Mathematics · #31C #47A #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #math.CV #math.FA #msc:31C #msc:47A
paper · pdf · doi:10.48550/arxiv.1610.03523
arxiv created 2016/10/11 · arxiv updated 2016/10/13
We propose to view hermitian metrics on trivial holomorphic vector bundles E→Ω as noncommutative analogs of functions defined on the base Ω, 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.