Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compactness of the space of embedded minimal surfaces with free boundary
  in three-manifolds with nonnegative Ricci curvature and convex boundary   We prove a lower bound for the first Steklov eigenvalue of embedded minimal
hypersurfaces with free boundary in a compact $n$-dimensional manifold which
has nonnegative Ricci curvature and strictly convex boundary. When $n=3$, this
implies apriori area and curvature estimates for these minimal surfaces in
terms of the geometry of the ambient manifold and the topology of the minimal
surface. An important consequence of the estimate is a smooth compactness
result for embedded minimal surfaces with free boundary when the topological
type of these minimal surfaces is fixed.

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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: stat
11
The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph