Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Boundary measures, generalized Gauss-Green formulas, and mean value
  property in metric measure spaces   We study mean value properties of harmonic functions in metric measure
spaces. The metric measure spaces we consider have a doubling measure and
support a (1,1)- Poincar\'e inequality. The notion of harmonicity is based on
the Dirichlet form defined in terms of a Cheeger differentiable structure. By
studying fine properties of the Green function on balls, we characterize
harmonic functions in terms of a mean value property. As a consequence, we
obtain a detailed description of Poisson kernels. We shall also obtain a
Gauss-Green type formula for sets of finite perimeter which posses a Minkowski
content characterization of the perimeter. For the Gauss-Green formula we
introduce a suitable notion of the interior normal trace of a regular ball.

21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph