On Asymptotic Isoperimetric Constant of Tori
نویسندگان
چکیده
In this note we continue the study of asymptotic invariants of Riemannian tori (e.g. see [BuI] and references there). By asymptotic invariants we mean invariants which do not change under passing to finite covers. In [BuI] we show that the asymptotic volume growth of a Riemannian torus is at least as fast as that of a flat one. One may ask what are the possible values of “asymptotic isoperimetric constants” for such metrics (see definition below). We show that the asymptotic isoperimetric constant of a conformally flat torus is no less than that of a flat one, while for general metrics (in dimensions higher than 2) this constant may be arbitrarily small. Let (M, g) be the universal cover of a Riemannian n-torus.
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