  Let $M$ be a complete Riemannian manifold, $N\in \NN$ and $p\ge 1$. We prove
that almost everywhere on $x=(x_1,...,x_N)\in M^N$ for Lebesgue measure in
$M^N$, the measure $\di \mu(x)=\f1N\sum_{k=1}^N\d_{x_k}$ has a unique $p$-mean
$e_p(x)$. As a consequence, if $X=(X_1,...,X_N)$ is a $M^N$-valued random
variable with absolutely continuous law, then almost surely $\mu(X(\om))$ has a
unique $p$-mean. In particular if $(X_n)_{n\ge 1}$ is an independent sample of
an absolutely continuous law in $M$, then the process
$e_{p,n}(\om)=e_p(X_1(\om),..., X_n(\om))$ is well-defined. Assume $M$ is
compact and consider a probability measure $\nu$ in $M$. Using partial
simulated annealing, we define a continuous semimartingale which converges to
the set of minimizers of the integral of distance at power $p$ with respect to
$\nu$. When the set is a singleton, it converges to the $p$-mean.
