Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local monotonicity of Riemannian and Finsler volume with respect to
  boundary distances   We show that the volume of a simple Riemannian metric on $D^n$ is locally
monotone with respect to its boundary distance function. Namely if $g$ is a
simple metric on $D^n$ and $g'$ is sufficiently close to $g$ and induces
boundary distances greater or equal to those of $g$, then $vol(D^n,g')\ge
vol(D^n,g)$. Furthermore, the same holds for Finsler metrics and the
Holmes--Thompson definition of volume. As an application, we give a new proof
of the injectivity of the geodesic ray transform for a simple Finsler metric.

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The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph