Finite Riemann surface

A Riemann surface of finite genus (cf. Genus of a surface) having finitely many non-degenerate boundary components. A finite Riemann surface can be imbedded in a closed Riemann surface — its double (cf. Double of a Riemann surface).

References

[1]	M. Schiffer, D.C. Spencer, "Functionals of finite Riemann surfaces" , Princeton Univ. Press (1954)

Comments

The notion of a finite Riemann surface should not be mixed up with that of a Riemann surface of finite type: A Riemann surface $M$ is of finite type if it can be imbedded in a compact Riemann surface $\tilde M$ such that $\tilde M \setminus M$ consists of finitely many points. Cf. also Riemann surfaces, classification of and (the references to) Double of a Riemann surface.