Suppose $H$ is subharmonic function in the $\bar{\mathbb{D}}^c$ (i.e., the complement of the unit disc in the complex plane) which is bounded (both above and below) and continuous up to the boundary. Can $H$ be non-constant? If it is possible, it will be good to have an example.
2026-03-25 17:28:20.1774459700
Bounded subharmonic function in the complement of unit disc
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