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arxiv: 1709.05754 · v1 · pith:52VJKTYDnew · submitted 2017-09-18 · 🧮 math.DG

A mean value formula and a Liouville theorem for the complex Monge-Amp\`ere equation

classification 🧮 math.DG
keywords complexequationformulaliouvillemeanmonge-amptheoremvalue
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In this paper, we prove a mean value formula for bounded subharmonic Hermitian matrix valued function on a complete Riemannian manifold with nonnegative Ricci curvature. As its application, we obtain a Liouville type theorem for the complex Monge-Amp\`ere equation on product manifolds.

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