On minimal higher genus fillings

In this article, we prove that if $(M,g)$ is a genus $G$ orientable surface with a single boundary component $S^1$, and if $(D,g_0)$ is a disc such that interior points are connected by unique geodesics and $d_{(D,g_0)}(x,y) \geq d_{(M,g)}(x,y)$ for all $x,y \in \partial M = \partial D$, then $(1 + \frac{2 G}π) \textrm{Area}(M,g) \geq \textrm{Area}(D,g_0).$

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