2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65056Let S be a bordered Riemann surface with genus g and m boundary components. For a smooth family of smooth Jordan curves in the complex plane parametrized by the boundary of S and such that all curves contain 0 in their interior we show that there exists a holomorphic solution of the corresponding Riemann-Hilbert problem with at most 2g+m-1 zeros on S.18 pagesComplex Variables30E25, 35Q15 (Primary) 32E20 (Secondary)text