Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The geometry of $C^{1,\alpha}$ flat isometric immersions   We show that any isometric immersion of a flat plane domain into $\mathbb
R^3$ is developable provided it enjoys the little H\"older regulairty
$c^{1,2/3}$. In particular, isometric immersions of local $C^{1,\alpha}$
regularity with $\alpha > 2/3$ belong to this class. The proof is based on the
existence of a weak notion of second fundamental form for such immersions, the
analysis of the Gauss-Codazzi-Mainardi equations in this weak setting, and a
parallel result on the very weak solutions to the degenerate Monge-Amp\`ere
equation analyzed by Lewicka and the second author.

13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an