  On a given arithmetic surface, inspired by work of Miyaoka, we consider
vector bundles which are extensions of a line bundle by another one. We give
sufficient conditions for their restriction to the generic fiber to be
semi-stable. We then apply the arithmetic analog of Bogomolov inequality in
Arakelov theory, and deduce from it a lower bound for some successive minima in
the lattice of extension classes between these line bundles.
