Asymptotic isoperimetry of balls in metric measure spaces

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dc.creatorTessera, R.
dc.date2005-06-17
dc.date2005-10-03
dc.date.accessioned2026-07-07T06:20:29Z
dc.date.available2026-07-07T06:20:29Z
dc.descriptionIn this paper, we study the asymptotic behavior of the volume of spheres in metric measure spaces. We first introduce a general setting adapted to the study of asymptotic isoperimetry in a general class of metric measure spaces. We then introduce a notion of "being asymptotically isoperimetric" for a family of finite and unbounded measure subsets. We show that there exist graphs with uniform polynomial growth whose balls are not asymptotically isoperimetric and we discuss the stability of related properties under quasi-isometries. Finally, we study the asymptotically isoperimetric properties of connected subsets in a metric measure space. In particular, we build graphs with uniform polynomial growth whose connected subsets are not asymptotically isoperimetric.
dc.identifierhttps://arxiv.org/abs/math/0506363
dc.identifierhttp://arxiv.org/abs/math/0506363
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/95339
dc.subjectMetric Geometry
dc.subjectGeometric Topology
dc.titleAsymptotic isoperimetry of balls in metric measure spaces
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