Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Riesz continuity of the Atiyah-Singer Dirac operator under perturbations
  of local boundary conditions   On a smooth complete Riemannian spin manifold with smooth compact boundary,
we demonstrate that the Atiyah-Singer Dirac operator $\mathrm{D}_{\mathcal B}$
in $\mathrm{L}^{2}$ depends Riesz continuously on $\mathrm{L}^{\infty}$
perturbations of local boundary conditions ${\mathcal B}$. The Lipschitz bound
for the map ${\mathcal B} \to {\mathrm{D}}_{\mathcal B}(1 +
{\mathrm{D}}_{\mathcal B}^2)^{-\frac{1}{2}}$ depends on Lipschitz smoothness
and ellipticity of ${\mathcal B}$ and bounds on Ricci curvature and its first
derivatives as well as a lower bound on injectivity radius. More generally, we
prove perturbation estimates for functional calculi of elliptic operators on
manifolds with local boundary conditions.

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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas