  The uniqueness of parabolic Cauchy problems is nowadays a classical problem
and since Hadamard \cite{Ha} these kind of problems are known to be ill-posed
and even severely ill-posed. Until now there are only few partial results
concerning the quantification of the stability for parabolic Cauchy problems.
In the present article, we bring the complete answer to this issue, provided
that the space domain has finite diameter with respect to the geodesic distance
and assuming that solutions are sufficiently smooth.
