JournalsjemsVol. 23, No. 1pp. 153–184

Deforming 3-manifolds of bounded geometry and uniformly positive scalar curvature

  • Laurent Bessières

    Université de Bordeaux, Talence, France
  • Gérard Besson

    Université Grenoble Alpes, Gières, France
  • Sylvain Maillot

    Université de Montpellier 2, France
  • Fernando C. Marques

    Princeton University, USA
Deforming 3-manifolds of bounded geometry and uniformly positive scalar curvature cover
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Abstract

We prove that the moduli space of complete Riemannian metrics of bounded geometry and uniformly positive scalar curvature on an orientable 3-manifold is path-connected. This generalises the main result of the fourth author [Mar12] in the compact case. The proof uses Ricci flow with surgery as well as arguments involving performing infinite connected sums with control on the geometry.

Cite this article

Laurent Bessières, Gérard Besson, Sylvain Maillot, Fernando C. Marques, Deforming 3-manifolds of bounded geometry and uniformly positive scalar curvature. J. Eur. Math. Soc. 23 (2021), no. 1, pp. 153–184

DOI 10.4171/JEMS/1008