Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Restriction Theorem for Fully Nonlinear Subequations   We address the restriction problem for viscosity subsolutions of a fully
nonlinear PDE on a manifold Z. The constraints on the restrictions of smooth
subsolutions to a submanifold X in Z determine a restricted subequation on X.
The problem is to show that general (upper semi-continuous) subsolutions
restrict to satisfy the same constraints. We first prove an elementary result
which, in theory, can be applied to any subequation. Then two definitive
results are obtained. The first applies to any "geometrically defined"
subequation, and the second to any subequation which can be transformed to a
constant coefficient (i.e., euclidean) model. This provides a long list of
geometrically and analytically interesting cases where restriction holds.

16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex