Derivative relationships between volume and surface area of compact regions in R^d

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dc.creatorMarichal, Jean-Luc
dc.creatorDorff, Michael
dc.date2007-02-22
dc.date.accessioned2026-07-07T08:08:42Z
dc.date.available2026-07-07T08:08:42Z
dc.descriptionWe explore the idea that the derivative of the volume, V, of a region in R^d with respect to r equals its surface area, A, where r = d V/A. We show that the families of regions for which this formula for r is valid, which we call homogeneous families, include all the families of similar regions. We determine equivalent conditions for a family to be homogeneous, provide examples of homogeneous families made up of non-similar regions, and offer a geometric interpretation of r in a few cases.
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/math/0702635
dc.identifierhttp://arxiv.org/abs/math/0702635
dc.identifierRocky Mountain Journal of Mathematics 37 (2) (2007) 551-571
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/131355
dc.subjectMetric Geometry
dc.subjectFunctional Analysis
dc.subject51M25, 52A38 (Primary) 26A24, 52B60 (Secondary)
dc.titleDerivative relationships between volume and surface area of compact regions in R^d
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