Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Frankel property for self-shrinkers from the viewpoint of elliptic
  PDE's   We show that two properly embedded self-shrinkers in Euclidean space that are
sufficiently separated at infinity must intersect at a finite point. The proof
is based on a localized version of the Reilly formula applied to a suitable
f-harmonic function with controlled gradient. In the immersed case, a new
direct proof of the generalized half-space property is also presented.

21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys