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Abstract:

We compare the isoperimetric profiles of S2×R3 and of S3×R2 with that of a round 5-sphere (of appropriate radius). Then we use this comparison to obtain lower bounds for the Yamabe constants of S2×R3 and S3×R2. Explicitly we show that Y(S3×R2,[g0 3+dx 2])>(3/4)Y(S5) and Y(S2×R3,[g0 2+dx 2])>0.63Y(S5). We also obtain explicit lower bounds in higher dimensions and for products of Euclidean space with a closed manifold of positive Ricci curvature. The techniques are a more general version of those used by the same authors in Petean and Ruiz (2011) [15] and the results are a complement to the work developed by B. Ammann, M. Dahl and E. Humbert to obtain explicit gap theorems for the Yamabe invariants in low dimensions. © 2013 Elsevier B.V.

Registro:

Documento: Artículo
Título:On the Yamabe constants of S2×R3 and S3×R2
Autor:Petean, J.; Ruiz, J.M.
Filiación:CIMAT, A.P. 402, 36000 Guanajuato, Gto, Mexico
Departamento de Matemáticas, FCEyN Universidad de Buenos Aires, Argentina
IMPA, Estrada Dona Castorina 110, CEP 22460-320, Rio de Janeiro, Brazil
Palabras clave:Isoperimetric profile; Yamabe constants
Año:2013
Volumen:31
Número:2
Página de inicio:308
Página de fin:319
DOI: http://dx.doi.org/10.1016/j.difgeo.2013.01.006
Título revista:Differential Geometry and its Application
Título revista abreviado:Differ. Geom. Appl.
ISSN:09262245
CODEN:DGAPE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09262245_v31_n2_p308_Petean

Referencias:

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  • Akutagawa, K., Neves, A., 3-Manifolds with Yamabe invariant greater than that of RP3 (2007) J. Differential Geom., 75, pp. 359-386
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  • Ammann, B., Dahl, M., Humbert, E., Square-integrability of solutions of the Yamabe equation, preprint arXiv.org math-DG.
  • Ammann, B., Dahl, M., Humbert, E., The conformal Yamabe constant of product manifolds (2013) Proc. Amer. Math. Soc., 141, pp. 295-307
  • Ammann, B., Dahl, M., Humbert, E., Low dimensional surgery and the Yamabe invariant, , arxiv:1204.1197, preprint
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Citas:

---------- APA ----------
Petean, J. & Ruiz, J.M. (2013) . On the Yamabe constants of S2×R3 and S3×R2. Differential Geometry and its Application, 31(2), 308-319.
http://dx.doi.org/10.1016/j.difgeo.2013.01.006
---------- CHICAGO ----------
Petean, J., Ruiz, J.M. "On the Yamabe constants of S2×R3 and S3×R2" . Differential Geometry and its Application 31, no. 2 (2013) : 308-319.
http://dx.doi.org/10.1016/j.difgeo.2013.01.006
---------- MLA ----------
Petean, J., Ruiz, J.M. "On the Yamabe constants of S2×R3 and S3×R2" . Differential Geometry and its Application, vol. 31, no. 2, 2013, pp. 308-319.
http://dx.doi.org/10.1016/j.difgeo.2013.01.006
---------- VANCOUVER ----------
Petean, J., Ruiz, J.M. On the Yamabe constants of S2×R3 and S3×R2. Differ. Geom. Appl. 2013;31(2):308-319.
http://dx.doi.org/10.1016/j.difgeo.2013.01.006