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- W2064065495 abstract "In (Comm. Math. Phys. 188 (1997) 121–133) Herzlich proved a new positive mass theorem for Riemannian 3-manifolds ( N , g ) whose mean curvature of the boundary allows some positivity. In this paper we study what happens to the limit case of the theorem when, at a point of the boundary, the smallest positive eigenvalue of the Dirac operator of the boundary is strictly larger than one-half of the mean curvature (in this case the mass m ( g ) must be strictly positive). We prove that the mass is bounded from below by a positive constant c ( g ), m ( g )⩾ c ( g ), and the equality m ( g )= c ( g ) holds only if, outside a compact set, ( N , g ) is conformally flat and the scalar curvature vanishes. The constant c ( g ) is uniquely determined by the metric g via a Dirac-harmonic spinor." @default.
- W2064065495 created "2016-06-24" @default.
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- W2064065495 date "2004-05-01" @default.
- W2064065495 modified "2023-09-29" @default.
- W2064065495 title "Remark on the limit case of positive mass theorem for manifolds with inner boundary" @default.
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- W2064065495 doi "https://doi.org/10.1016/j.difgeo.2003.12.002" @default.
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