Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inverse mean curvature flows in warped product manifolds   We study inverse mean curvature flows of starshaped, mean convex
hypersurfaces in warped product manifolds with a positive warping factor
$\varphi(r)$. If $\varphi'(r)>0$ and $\varphi''(r)\geq 0$, we show that these
flows exist for all times, remain starshaped and mean convex. Plus the
positivity of $\varphi''(r)$ and a curvature condition we obtain a lower
positive bound of mean curvature along these flows independent of the initial
mean curvature. We also give a sufficient condition to extend the asymptotic
behavior of these flows in Euclidean spaces into some more general warped
product manifolds.

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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
18
The categories of this paper are: econ
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
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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: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg