Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Radial Deformations and Cavitation in Riemannian Manifolds with
  Applications to Membrane Shells   This study is a geometric version of Ball's work, Philos. Trans. Roy. Soc.
London Ser. A 306 (1982), no. 1496, 557-611. Radial deformations in Riemannian
manifolds are singular solutions to some nonlinear equations given by
constitutive functions and radial curvatures. A geodesic spherical cavity forms
at the center of a geodesic ball in tension by means of given surface tractions
or displacements. The existence of such solutions depends on the growth
properties of the constitutive functions and the radial curvatures.
  Some close relationships are shown among radial curvature, the constitutive
functions, and the behavior of bifurcation of a singular solution from a
trivial solution. In the incompressible case the bifurcation depends on the
local properties of the radial curvature near the geodesic ball center but the
bifurcation in compressible case is determined by the global properties of the
radial curvatures.
  A cavity forms at the center of a membrane shell of isotropic material placed
in tension by means of given boundary tractions or displacements when the
Riemannian manifold under question is a surface of $\R^3$ with the induced
metric. In addition, cavitation at the center of ellipsoids of $\R^n$ is also
described if the Riemannian manifold under question is $(\R^n g)$ where $g(x)$
are symmetric, positive matrices for $x\in\R^n.$

31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph