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Jan 27, 2020 at 3:36 comment added Yeah I realized that boundary critical points are isolated if we add Lagrangian/ totally real boundary condition. This is due to a similar similarity principle as interior points. Since I only care about holomorphic disks bounded by a Lagrangian submanifold, it’s all done.
Jan 23, 2020 at 5:52 comment added Jonny Evans My guess is that the answer is yes, but I don't know for sure.
Jan 23, 2020 at 3:38 vote accept Yeah
Jan 23, 2020 at 2:49 comment added Yeah Thank you Jonny! I now understand. Actually I am thinking about a seemingly harder question: if $u:D\to M$ is nonconstant pseudoholomorphic, then does $u|_{\partial D}$ have only (finitely many) isolated critical points? May I ask if you have an idea about this?
Jan 23, 2020 at 0:45 history answered Jonny Evans CC BY-SA 4.0