  Let $L\subset J^1(M)$ be a Legendrian submanifold of the 1-jet space of a
Riemannian $n$-manifold $M$. A correspondence is established between rigid flow
trees in $M$ determined by $L$ and boundary punctured rigid pseudo-holomorphic
disks in $T^\ast M$, with boundary on the projection of $L$ and asymptotic to
the double points of this projection at punctures, provided $n\le 2$, or
provided $n>2$ and the front of $L$ has only cusp edge singularities. This
result, in particular, shows how to compute the Legendrian contact homology of
$L$ in terms of Morse theory.
