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Second Yamabe Constant on Riemannian Products

URN to cite this document:
urn:nbn:de:bvb:355-epub-331479
DOI to cite this document:
10.5283/epub.33147
Henry, Guillermo
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Date of publication of this fulltext: 12 Jan 2016 12:50



Abstract

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 $\lim_{t \to +\infty}Y^2(M\times N,[g+th])=2^{\frac{2}{m+n}}Y(M\times \re^n, [g+g_e]).$ If n≥2, we show the existence of nodal solutions of the ...

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