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--- subharmonic_function [2022/09/03 06:43] – created spencer
+++ subharmonic_function [2022/09/03 06:47] (current) – spencer
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 ====== Subharmonic function ======
-A subharmonic function on a Riemannian manifold $M$ is a function $f : M \to \R$ with $\Delta f = \mathrm{d}^* \mathrm{d}f \le 0$.
+A subharmonic function on a Riemannian manifold $M$ is a function $f : M \to \mathbb{R}$ with $\Delta f = \mathrm{d}^* \mathrm{d}f \le 0$.
+Subharmonic functions satisfy the **maximum principle**: if a subharmonic function $f$ attains its maximum at an interior point of a domain of $M$, then $f$ is constant.