On minimal higher genus fillings

In this article, we extend a result of S. Ivanov to prove that if [Formula: see text] is a genus [Formula: see text] orientable surface with a single boundary component [Formula: see text], and if [Formula: see text] is a disc such that interior points are connected by unique minimizing geodesics and [Formula: see text] for all [Formula: see text], then [Formula: see text]