Counting minimal surfaces in negatively curved 3-manifolds

Danny Calegari; Fernando C. Marques; André Neves

doi:10.1215/00127094-2021-0057

1 June 2022 Counting minimal surfaces in negatively curved 3-manifolds

Danny Calegari, Fernando C. Marques, André Neves

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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 $\le -1$ , by the hyperbolic metric.

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Danny Calegari. Fernando C. Marques. André Neves. "Counting minimal surfaces in negatively curved 3-manifolds." Duke Math. J. 171 (8) 1615 - 1648, 1 June 2022. https://doi.org/10.1215/00127094-2021-0057

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Received: 19 May 2020; Revised: 16 February 2021; Published: 1 June 2022

First available in Project Euclid: 10 May 2022

MathSciNet: MR4432012

zbMATH: 1502.53094

Digital Object Identifier: 10.1215/00127094-2021-0057

Subjects:

Primary: 53A10

Keywords: hyperbolic manifolds , minimal surfaces

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