M. Lesourd - Positive Scalar Curvature on Noncompact Manifolds and the Positive Mass Theorem

Martin Lesourd (1) , Fanny Bastien (2) , Hugo Béchet (2)

1 Harvard University
2 IF - Institut Fourier

The study of positive scalar curvature on noncompact manifolds has seen significant progress in the last few years. A major role has been played by Gromov's results and conjectures, and in particular the idea to use surfaces of prescribed mean curvature (as opposed to minimal surfaces). Having the classic positive mass theorem of Schoen-Yau in mind, we describe a new positive mass theorem for manifolds that allows for possibly non asymptotically flat ends, points of incompleteness, and regions negative scalar curvature. The proof is based on surfaces with prescribed mean curvature, and gives an alternative proof of the Liouville theorem conjectured by Schoen-Yau, which was recently proved by Chodosh-Li. This is joint with R.Unger and S-T. Yau.

Mots clés: positive scalar; noncompact manifolds; positive mass theorem; eem2021; grenoble; curvature constraints and spaces of metrics

Mots clés: contraintes de courbures et espaces métriques

Domaines: Mathématiques [math]

Martin Lesourd, Fanny Bastien, Hugo Béchet. M. Lesourd - Positive Scalar Curvature on Noncompact Manifolds and the Positive Mass Theorem: Summer School 2021 - Curvature Constraints and Spaces of Metrics. 2021. ⟨hal-03322426⟩