Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Remark on the Limit Case of Positive Mass Theorem for Manifolds with
  Inner Boundary   In [5] 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 $c(g), m(g) \geq c(g)$, 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.

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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
5
The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: eess