A bounded domain $\Omega$ with smooth boundary $\Gamma$ can be considered as a compact connect Riemannian manifold?
2026-04-02 03:15:06.1775099706
A bounded domain can be considered as a compact manifold?
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Domains are open, so not compact. If you throw in the boundary to make it compact, it will no longer be a manifold (though it will be a manifold with boundary, since $\Gamma$ is smooth).