Morse flow trees and Legendrian contact homology in 1-jet spaces

Let L subset of 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 * M, with boundary on the projection of L and asymptotic to the double points of this projection at punctures, provided n <= 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.