Noncommutative potential theory

Laszlo Lempert

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arXiv · 1610.03523

Noncommutative potential theory

Laszlo Lempert

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Abstract

We propose to view hermitian metrics on trivial holomorphic vector bundles $E\to\Omega$ as noncommutative analogs of functions defined on the base $\Omega$, and curvature as the notion corresponding to the Laplace operator or $\partial\overline\partial$. We discuss noncommutative generalizations of basic results of ordinary potential theory, mean value properties, maximum principle, Harnack inequality, and the solvability of Dirichlet problems.

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Laszlo Lempert. 2016-10-11. Noncommutative potential theory. https://arxiv.org/abs/1610.03523

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