In McDuff & Salamon's book "J-holomorphic Curves and Symplectic Topology", only the Gromov compactness for spheres has been proved, and I wonder whether or not this compactness result is still true for genus $g>0$ Riemann surfaces.

If there does exist such a generalization of Gromov compactness, then does there exist any reference that contains detailed proof of it? It seems that the techniques used in this book are hard to apply for the case of arbitrary genus.

I prefer a proof using the notion of stable maps as in this book.

"Gromov's compactness theorem for pseudo holomorphic curves"by Rugang Ye (reference 310 of that book). Also see"Pseudo-holomorphic maps and bubble trees"by Parker-Wolfson. $\endgroup$