Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Natural boundary conditions in geometric calculus of variations   In this paper we obtain natural boundary conditions for a large class of
variational problems with free boundary values. In comparison with the already
existing examples, our framework displays complete freedom concerning the
topology of $Y$, the manifold of dependent and independent variables underlying
a given problem, as well as the order of its Lagrangian. Our result follows
from the natural behavior, under boundary-friendly transformations, of an
operator, similar to the Euler map, constructed in the context of relative
horizontal forms on jet bundles (or Grassmann fibrations) over $Y$. Explicit
examples of natural boundary conditions are obtained when $Y$ is an
$(n+1)$--dimensional domain in $\R^{n+1}$, and the Lagrangian is first-order
(in particular, the hypersurface area).

29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga