Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $C^{1,\alpha}$ Isometric Embeddings of Polar Caps   We study isometric embeddings of $C^2$ Riemannian manifolds in the Euclidean
space and we establish that the H\"older space $C^{1,\frac{1}{2}}$ is critical
in a suitable sense: in particular we prove that for $\alpha > \frac{1}{2}$ the
Levi-Civita connection of any isometric immersion is induced by the Euclidean
connection, whereas for any $\alpha < \frac{1}{2}$ we construct $C^{1,\alpha}$
isometric embeddings of portions of the standard $2$-dimensional sphere for
which such property fails.

31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys