Quasirational mappings on parabolic Riemann surfaces

fr,po LlrNn, Quasirational mappings on parabolic Riemann surfaces A region O on a Riemann surface -B is said to be regular, if O is compact, if the relative boundary ä() consists of a finite number of analSrtic Jordan curves and if R -I contains only non-compact components.We frequentlv use the following important lemma ([17], p. 25).Lemma 3. On an open Riemann surfa,ce R there eri,sts an erhaustion of R by regular regions Qr, ,i,.e.§,c Q,*, and, |jO,:n.Lemma 4. A closed set E on a parabolic ,ur"":'n is ytolar if and, only