Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pointwise differentiability of higher order for sets   The present paper develops two concepts of pointwise differentiability of
higher order for arbitrary subsets of Euclidean space defined by comparing
their distance functions to those of smooth submanifolds. Results include that
differentials are Borel functions, higher order rectifiability of the set of
differentiability points, and a Rademacher result. One concept is characterised
by a limit procedure involving inhomogeneously dilated sets.
  The original motivation to formulate the concepts stems from studying the
support of stationary integral varifolds. In particular, strong pointwise
differentiability of every positive integer order is shown at almost all points
of the intersection of the support with a given plane.

6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys