Second Yamabe constant on Riemannian products

Let (Mm,g) be a closed Riemannian manifold (m≥2) of positive scalar curvature and (Nn,h) any closed manifold. We study the asymptotic behaviour of the second Yamabe constant and the second N-Yamabe constant of (M×N,g+th) as t goes to +∞. We obtain that limt→+∞Y2(M×N,[g+th])=22m+nY(M×Rn,[g+ge]). If n...

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Detalles Bibliográficos
Autor principal: Henry, Guillermo Sebastián
Publicado: 2017
Materias:
Nodal solutions
Second Yamabe constant
Yamabe equation
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03930440_v114_n_p260_Henry
http://hdl.handle.net/20.500.12110/paper_03930440_v114_n_p260_Henry
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_03930440_v114_n_p260_Henry
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spelling paper:paper_03930440_v114_n_p260_Henry2023-06-08T15:41:01Z Second Yamabe constant on Riemannian products Henry, Guillermo Sebastián Nodal solutions Second Yamabe constant Yamabe equation Let (Mm,g) be a closed Riemannian manifold (m≥2) of positive scalar curvature and (Nn,h) any closed manifold. We study the asymptotic behaviour of the second Yamabe constant and the second N-Yamabe constant of (M×N,g+th) as t goes to +∞. We obtain that limt→+∞Y2(M×N,[g+th])=22m+nY(M×Rn,[g+ge]). If n≥2, we show the existence of nodal solutions of the Yamabe equation on (M×N,g+th) (provided t large enough). When sg is constant, we prove that limt→+∞YN 2(M×N,g+th)=22m+nYRn(M×Rn,g+ge). Also we study the second Yamabe invariant and the second N-Yamabe invariant. © 2016 Elsevier B.V. Fil:Henry, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2017 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03930440_v114_n_p260_Henry http://hdl.handle.net/20.500.12110/paper_03930440_v114_n_p260_Henry
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Nodal solutions
Second Yamabe constant
Yamabe equation
spellingShingle Nodal solutions
Second Yamabe constant
Yamabe equation
Henry, Guillermo Sebastián
Second Yamabe constant on Riemannian products
topic_facet Nodal solutions
Second Yamabe constant
Yamabe equation
description Let (Mm,g) be a closed Riemannian manifold (m≥2) of positive scalar curvature and (Nn,h) any closed manifold. We study the asymptotic behaviour of the second Yamabe constant and the second N-Yamabe constant of (M×N,g+th) as t goes to +∞. We obtain that limt→+∞Y2(M×N,[g+th])=22m+nY(M×Rn,[g+ge]). If n≥2, we show the existence of nodal solutions of the Yamabe equation on (M×N,g+th) (provided t large enough). When sg is constant, we prove that limt→+∞YN 2(M×N,g+th)=22m+nYRn(M×Rn,g+ge). Also we study the second Yamabe invariant and the second N-Yamabe invariant. © 2016 Elsevier B.V.
author Henry, Guillermo Sebastián
author_facet Henry, Guillermo Sebastián
author_sort Henry, Guillermo Sebastián
title Second Yamabe constant on Riemannian products
title_short Second Yamabe constant on Riemannian products
title_full Second Yamabe constant on Riemannian products
title_fullStr Second Yamabe constant on Riemannian products
title_full_unstemmed Second Yamabe constant on Riemannian products
title_sort second yamabe constant on riemannian products
publishDate 2017
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03930440_v114_n_p260_Henry
http://hdl.handle.net/20.500.12110/paper_03930440_v114_n_p260_Henry
work_keys_str_mv AT henryguillermosebastian secondyamabeconstantonriemannianproducts
_version_ 1768544455965540352

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