Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Riemannian geometry on spaces of submanifolds induced by the
  diffeomorphism group   The space of embedded submanifolds plays an important role in applications
such as computational anatomy and shape analysis. We can define two different
classes on Riemannian metrics on this space: so-called outer metrics are
metrics that measure shape changes using deformations of the ambient space and
they find applications mostly in computational anatomy; the second class that
are defined directly on the space of embeddings using intrinsic differential
operations and they are used in shape analysis. In this paper we compare for
the first time the topologies and the geodesic distance functions induced by
these the two classes of metrics.

10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an