The sharp isoperimetric inequality for minimal surfaces with radially connected boundary in hyperbolic space (Q1803378)

Let \(\Sigma\) be a two-dimensional minimal surface in the \(n\)-dimensional hyperbolic space \(H^ n\). Assume that the boundary \(\partial\Sigma\) of \(\Sigma\) is radially connected from some point \(p\) of \(\Sigma\), that is, \(\{r=\text{dist}(p,q),q\in\partial\Sigma\}\) is a connected interval. Then the authors obtain a sharp isoperimetric inequality \(4\pi A\leq L^ 2- A^ 2\), where \(L\) is the length of \(\partial\Sigma\) and \(A\) is the area of \(\Sigma\).