%0 Journal Article
%T Local monotonicity of Riemannian and Finsler volume with respect to boundary distances
%A Sergei Ivanov
%J Mathematics
%D 2011
%I arXiv
%R 10.1007/s10711-012-9760-y
%X 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.
%U http://arxiv.org/abs/1109.4091v3