Counting essential minimal surfaces in closed negatively curved n-manifolds

Abstract

For closed odd-dimensional manifolds with sectional curvature less or equal than -1, we define the minimal surface entropy that counts the number of surface subgroups. It attains the minimum if and only if the metric is hyperbolic. Moreover, we compute the entropy associated with other locally symmetric spaces and cusped hyperbolic 3-manifolds.

18 pages; references corrected. Comments are welcome!

References in corpus (4)

• Nearly Fuchsian surface subgroups of finite covolume Kleinian groups
• Orbit closures of unipotent flows for hyperbolic manifolds with Fuchsian ends
• Counting Essential Surfaces in a Closed Hyperbolic 3-Manifold
• Minimal Surfaces in Quasi-Fuchsian 3-Manifolds