February 2024 Constrained deformations of positive scalar curvature metrics
Alessandro Carlotto, Chao Li
Author Affiliations +
J. Differential Geom. 126(2): 475-554 (February 2024). DOI: 10.4310/jdg/1712344218


We present a series of results concerning the interplay between the scalar curvature of a manifold and the mean curvature of its boundary. In particular, we give a complete topological characterization of those compact $3$-manifolds that support Riemannian metrics of positive scalar curvature and mean-convex boundary and, in any such case, we prove that the associated moduli space of metrics is path-connected. The methods we employ are flexible enough to allow the construction of continuous paths of positive scalar curvature metrics with minimal boundary, and to derive similar conclusions in that context as well. Our work relies on a combination of earlier fundamental contributions by Gromov–Lawson and Schoen–Yau, on the smoothing procedure designed by Miao, and on the interplay of Perelman’s Ricci flow with surgery and conformal deformation techniques introduced by Codá Marques in dealing with the closed case.


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Alessandro Carlotto. Chao Li. "Constrained deformations of positive scalar curvature metrics." J. Differential Geom. 126 (2) 475 - 554, February 2024. https://doi.org/10.4310/jdg/1712344218


Received: 16 September 2019; Accepted: 12 October 2021; Published: February 2024
First available in Project Euclid: 5 April 2024

Digital Object Identifier: 10.4310/jdg/1712344218

Rights: Copyright © 2024 Lehigh University


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Vol.126 • No. 2 • February 2024
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