Geometriae Dedicata

, Volume 168, Issue 1, pp 291–310 | Cite as

On the magnitude of spheres, surfaces and other homogeneous spaces

  • Simon WillertonEmail author
Original Paper


In this paper we calculate the magnitude of metric spaces using measures rather than finite subsets as had been done previously. An explicit formula for the magnitude of an \(n\)-sphere with its intrinsic metric is given. For an arbitrary homogeneous Riemannian manifold the leading terms of the asymptotic expansion of the magnitude are calculated and expressed in terms of the volume and total scalar curvature of the manifold.


Magnitude Metric spaces Lipschitz-Killing curvatures 

Mathematics Subject Classification (2010)




It is a pleasure to thank Jonathan Jordan, Tom Leinster and David Speyer for their contributions to Sect. 2, as well as for other informative discussions. I would also like to thank Mark Meckes for useful comments and conversations.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.School of Mathematics and Statistics, University of SheffieldSheffieldUK

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