compact Riemann surface
英[kəmˈpækt ˈri:mɑ:n ˈsə:fis]美[kəmˈpækt ˈrimən ˈsɚfəs]
In mathematics, a compact Riemann surface is a complex manifold of dimension one that is a compact space. Riemann surfaces are generally classified first into the compact (those that are closed manifolds) and the open (the rest, which from the point of view of complex analysis are very different, being for example Stein manifolds).