Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniform boundedness principles for Sobolev maps into manifolds   Given a connected Riemannian manifold $\mathcal{N}$, an \(m\)--dimensional
Riemannian manifold $\mathcal{M}$ which is either compact or the Euclidean
space, $p\in [1, +\infty)$ and $s\in (0,1]$, we establish, for the problems of
surjectivity of the trace, of weak-bounded approximation, of lifting and of
superposition, that qualitative properties satisfied by every map in a
nonlinear Sobolev space $W^{s,p}(\mathcal{M}, \mathcal{N})$ imply corresponding
uniform quantitative bounds. This result is a nonlinear counterpart of the
classical Banach--Steinhaus uniform boundedness principle in linear Banach
spaces.

31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg