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- W2103058188 abstract "We study the Yamabe invariants of cylindrical manifolds and compact orbifolds with a finite number of singularities, by means of conformal geometry and the Atiyah-Patodi-Singer $L^2$-index theory. For an $n$-orbifold $M$ with singularities $Sigma_{Gamma} = {(check{p}_1, Gamma_1), ..., (check{p}_s, Gamma_s)}$ (where each group $Gamma_j<O(n)$ is of finite order), we define and study the emph{orbifold Yamabe invariant} $Y^{orb}(M)$. We prove that $Y^{orb}(M)$ coincides with the corresponding $h$-$emph{cylindrical Yamabe invariant}$ $Y^{htextrm{-}cyl}(M setminus {check{p}_1, ..., check{p}_s})$ defined by the authors cite{AB2}, where $h = h_{Gamma_j}$ is the standard metric on the slice $S^{n-1}/Gamma_j$ of each end with infinity $check{p}_j$. Using this, we show that $Y^{orb}(M)$ is bounded by $Y(S^n) /d$ from above, where $d=max_j|Gamma_j|^{frac{2}{n}}$. For a cylindrical 4-manifold $X$ with a general slice metric $h$ on the end, we also establish a method for estimating the $h$-cylindrical Yamabe invariant $Y^{htextrm{-}cyl}(X)$ from above, in terms of the geometry and topology of $X$. We conclude by an explicit estimate of $Y^{htextrm{-}cyl}(X)$ for particular cylindrical 4-manifolds $X$, including that of $Y^{orb}(M)$ for 4-orbifolds $M$." @default.
- W2103058188 created "2016-06-24" @default.
- W2103058188 creator A5000631477 @default.
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- W2103058188 date "2002-04-05" @default.
- W2103058188 modified "2023-09-27" @default.
- W2103058188 title "The Yamabe invariants of orbifolds and cylindrical manifolds, and $L^2$-harmonic spinors" @default.
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