Counting minimal surfaces in negatively curved 3-manifolds
Danny Calegari, Fernando C. Marques, André Neves
Abstract
We introduce an asymptotic quantity that counts area-minimizing surfaces in negatively curved closed 3-manifolds and show that quantity to only be minimized, among all metrics of sectional curvature ≤−1, by the hyperbolic metric.
Topics & Concepts
MathematicsSectional curvatureMetric (unit)CurvaturePure mathematicsGeometryMathematical analysisScalar curvatureOperations managementEconomicsGeometric Analysis and Curvature FlowsGeometric and Algebraic TopologyMathematical Dynamics and Fractals