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Sep 21, 2022 at 4:06 history edited Alexandre Eremenko CC BY-SA 4.0
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Sep 2, 2022 at 22:15 history edited Alexandre Eremenko CC BY-SA 4.0
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Sep 2, 2022 at 18:59 comment added Alexandre Eremenko It is parabolic (before you remove the disk) in the sense that there is no Green function. So your new question is: suppose that a surface has a Green function. Does there exist a function with a single pole which is bounded outside a neighborhood of this pole? I suppose that the answer is still negative but do not have a ready example.
Sep 2, 2022 at 18:32 comment added Lukasz Kosinski Thanks a lot for your answer! Can I have one more question? I took a quick look at the paper and it seems that the surface constructed there is parabolic. Can I ask about the answer within the class of hyperbolic Riemann surfaces?
Sep 2, 2022 at 17:35 vote accept Lukasz Kosinski
Sep 2, 2022 at 17:04 history answered Alexandre Eremenko CC BY-SA 4.0