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A comment on Liu and Yau's positive quasi-local mass

Abstract:
Liu and Yau (Phys.Rev.Lett. 90, 231102, 2003) propose a definition of quasi-local mass for any space-like, topological 2-sphere with positive Gauss curvature (and subject to a second, convexity, condition). They are able to show it is positive using a result of Shi and Tam (J.Diff.Geom. 62, 79, 2002). However, as we show here, their definition can give a strictly positive mass for a sphere in flat space.

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Publication date:
2004-06-25
URN:
uuid:aa380f70-098b-4040-9dd3-41cd5e1e2c7d
Local pid:
oai:eprints.maths.ox.ac.uk:136

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