With the above choice of $v$ assume that the metric satisfies for any $z\in\partial U_{1}$ the condition

where $e_{z}\in T_{z}B$ is the unit tangent vector to $\partial U_{1}$ and $n_{z}$ is the normal vector to $\partial U_{1}$ (all scalar products and lengths are taken with respect to the metric $g$).

Then there exists $C>0$ such that

for all $(z,P)\in{\cal M}$.