• Corpus ID: 231846894

Area, Scalar Curvature, and Hyperbolic 3-Manifolds

  title={Area, Scalar Curvature, and Hyperbolic 3-Manifolds},
  author={Ben Lowe},
  • Ben Lowe
  • Published 6 February 2021
  • Mathematics
Let M be a closed hyperbolic 3-manifold that contains a closed immersed totally geodesic surface Σ. Then if g is a Riemannian metric on M with scalar curvature greater than or equal to −6, we show that the area in g of any surface homotopic to Σ is greater than or equal to the area of Σ in the hyperbolic metric, with equality only if g is isometric to the hyperbolic metric. We also consider a functional introduced by Calegari-MarquesNeves that is defined by an asymptotic count of minimal… 
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