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Symmetry, Integrability and Geometry: Methods and Applications, 2023, Volume 19, 027, 11 pp.
DOI: https://doi.org/10.3842/SIGMA.2023.027 (Mi sigma1922) 		 
Yamabe Invariants, Homogeneous Spaces, and Rational Complex Surfaces

Claude LeBrun

Department of Mathematics, Stony Brook University, Stony Brook, NY 11794-3651, USA
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DOI: https://doi.org/10.3842/SIGMA.2023.027
Abstract: The Yamabe invariant is a diffeomorphism invariant of smooth compact manifolds that arises from the normalized Einstein–Hilbert functional. This article highlights the manner in which one compelling open problem regarding the Yamabe invariant appears to be closely tied to static potentials and the first eigenvalue of the Laplacian.
Keywords: scalar curvature, conformal structure, Yamabe problem, diffeomorphism invariant.
Funding agency Grant number
National Science Foundation DMS–2203572
This research was supported in part by NSF grant DMS–2203572.
Received: February 23, 2023; in final form May 2, 2023; Published online May 7, 2023
Bibliographic databases:
Document Type: Article
MSC: 53C21, 53C18, 14J26, 58J50
Language: English
Citation: Claude LeBrun, “Yamabe Invariants, Homogeneous Spaces, and Rational Complex Surfaces”, SIGMA, 19 (2023), 027, 11 pp.
Citation in format AMSBIB
\Bibitem{Leb23}
\by Claude~LeBrun
\paper Yamabe Invariants, Homogeneous Spaces, and Rational Complex Surfaces
\jour SIGMA
\yr 2023
\vol 19
\papernumber 027
\totalpages 11
\mathnet{http://mi.mathnet.ru/sigma1922}
\crossref{https://doi.org/10.3842/SIGMA.2023.027}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4584275}
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