  We prove new concentration estimates for random variables that are
functionals of a Poisson measure defined on a general measure space. Our
results are specifically adapted to geometric applications, and are based on a
pervasive use of a powerful logarithmic Sobolev inequality proved by L. Wu
(2000), as well as on several variations of the so-called Herbst argument. We
provide several applications, in particular to edge counting and more general
length power functionals in random geometric graphs, as well as to the convex
distance for random point measures recently introduced by M. Reitzner (2013).
