Workshop on "Teichmüller theory and surfaces in 3-manifolds"

Closed minimal surfaces in quasi-Fuchsian manifolds

speaker: Andy Huang (Rice University)

abstract: It is well-known that each quasi-Fuchsian manifold contains at least one closed incompressible minimal surface. An intriguing question is how many? Understanding these minimal surfaces turns out to have many applications in Teichmuller theory, hyperbolic three-manifolds and other fields. In joint work with Biao Wang, we partially answer above question. A very short answer is the supremum over all quasi-Fuchsian manifolds of all genera at least two is positive infinity.

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