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Symmetry, Integrability and Geometry: Methods and Applications, 2024, Volume 20, 014, 13 pp.
DOI: https://doi.org/10.3842/SIGMA.2024.014 (Mi sigma2016) 		 
A Note about Isotopy and Concordance of Positive Scalar Curvature Metrics on Compact Manifolds with Boundary

Alessandro Carlottoa, Chao Lib

a Università di Trento, Dipartimento di Matematica, via Sommarive 14, 38123 Trento, Italy
b New York University – Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA
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DOI: https://doi.org/10.3842/SIGMA.2024.014
Abstract: We study notions of isotopy and concordance for Riemannian metrics on manifolds with boundary and, in particular, we introduce two variants of the concept of minimal concordance, the weaker one naturally arising when considering certain spaces of metrics defined by a suitable spectral “stability” condition. We develop some basic tools and obtain a rather complete picture in the case of surfaces.
Keywords: positive scalar curvature, isotopy, concordance, free boundary minimal surfaces.
Funding agency Grant number
European Research Council 947923
National Science Foundation DMS-2202343
This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 947923). C.L. was supported by an NSF grant (DMS-2202343).
Received: July 3, 2023; in final form January 31, 2024; Published online February 13, 2024
Document Type: Article
MSC: 53C21, 53A10
Language: English
Citation: Alessandro Carlotto, Chao Li, “A Note about Isotopy and Concordance of Positive Scalar Curvature Metrics on Compact Manifolds with Boundary”, SIGMA, 20 (2024), 014, 13 pp.
Citation in format AMSBIB
\Bibitem{CarLi24}
\by Alessandro~Carlotto, Chao~Li
\paper A Note about Isotopy and Concordance of Positive Scalar Curvature Metrics on Compact Manifolds with Boundary
\jour SIGMA
\yr 2024
\vol 20
\papernumber 014
\totalpages 13
\mathnet{http://mi.mathnet.ru/sigma2016}
\crossref{https://doi.org/10.3842/SIGMA.2024.014}
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