# Area, Scalar Curvature, and Hyperbolic 3-Manifolds

@inproceedings{Lowe2021AreaSC, title={Area, Scalar Curvature, and Hyperbolic 3-Manifolds}, author={Ben Lowe}, year={2021} }

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…

## One Citation

MINIMAL SURFACE ENTROPY OF NEGATIVELY CURVED MANIFOLDS

- 2021

In this paper we discuss the minimal surface entropy introduced recently by the authors and propose a conjecture.

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