Title: Minimal surfaces near short geodesics in hyperbolic $3$-manifolds,
Abstract: If $M$ is a finite volume complete hyperbolic $3$-manifold, the quantity
$\mathcal A_1(M)$ is defined as the infimum of the areas of closed minimal
surfaces in $M$. In this paper we study the continuity property of the
functional $\mathcal A_1$ with respect to the geometric convergence of
hyperbolic manifolds. We prove that it is lower semi-continuous and even
continuous if $\mathcal A_1(M)$ is realized by a minimal surface satisfying
some hypotheses. Understanding the interaction between minimal surfaces and
short geodesics in $M$ is the main theme of this paper