Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Closed surfaces with different shapes that are indistinguishable by the
  SRNF   The Square Root Normal Field (SRNF), introduced by Jermyn et al. in [3],
provides a way of representing immersed surfaces in $\mathbb R^3$, and
equipping the set of these immersions with a "distance function" (to be
precise, a pseudometric) that is easy to compute. Importantly, this distance
function is invariant under reparametrizations (i.e., under
self-diffeomorphisms of the domain surface) and under rigid motions of $\mathbb
R^3$. Thus, it induces a distance function on the shape space of immersions,
i.e., the space of immersions modulo reparametrizations and rigid motions of
$\mathbb R^3$. In this paper, we give examples of the degeneracy of this
distance function, i.e., examples of immersed surfaces (some closed and some
open) that have the same SRNF, but are not the same up to reparametrization and
rigid motions. We also prove that the SRNF does distinguish the shape of a
standard sphere from the shape of any other immersed surface, and does
distinguish between the shapes of any two embedded strictly convex surfaces.

1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn