Background: In the paper with Fukaya ``Zero loop open strings in the cotangent bundle and Morse homotopy'', Asian J. Math. 1 (1997), 96 - 180, we proved that
``The moduli
space of holomorphic polygons with boundary lying on 
-tuples of
Lagrangian
graphs of -Morse functions is diffeomorphic to that of graph flows of
the Morse functions in the adiabatic limit or (in the large complex
structure limit).
The projections, near the limit, of the holomorphic polygons on the base
of
the cotangent bundle resembles
amoeba-type shapes and it shrinks to the graphs of Morse flows in the
limit.''
In the paper, we dealt with the case of discs, i.e., open Riemann surfaces of genus zero.
Problem: Study the similar degeneration problem for the higher genus case.
(contributed by Yong-Geun Oh)
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