Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Differentiable Rigidity under Ricci curvature lower bound   In this article we prove a differentiable rigidity result. Let $(Y, g)$ and
$(X, g_0)$ be two closed $n$-dimensional Riemannian manifolds ($n\geqslant 3$)
and $f:Y\to X$ be a continuous map of degree $1$. We furthermore assume that
the metric $g_0$ is real hyperbolic and denote by $d$ the diameter of
$(X,g_0)$. We show that there exists a number $\varepsilon:=\varepsilon (n,
d)>0$ such that if the Ricci curvature of the metric $g$ is bounded below by
$-n(n-1)$ and its volume satisfies $\vol_g (Y)\leqslant (1+\varepsilon)
\vol_{g_0} (X)$ then the manifolds are diffeomorphic. The proof relies on
Cheeger-Colding's theory of limits of Riemannian manifolds under lower Ricci
curvature bound.

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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex