For each , we prove existence of a computable constant such that if is a strongly irreducible Heegaard surface of genus in a complete hyperbolic –manifold and is a simple geodesic of length less than in , then is isotopic into .
William Breslin. "Short geodesics in hyperbolic $3$–manifolds." Algebr. Geom. Topol. 11 (2) 735 - 745, 2011. https://doi.org/10.2140/agt.2011.11.735