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It is known from the work of Deligne and Mumford that the "space" of punctured/marked Riemann surfaces is a Deligne-Mumford stack. I have few questions regarding similar statement for the spaces of surfaces with borders instead of puncture

  • What is the structure of the space of bordered Riemann surfaces? Is it still a stack? Is it a Deligne-Mumford stack?

  • What is the structure of the space of bordered spin- or super-Riemann curves? Are they stack? Are they Deligne-Mumford (super)stacks?

  • It is said that the space of bordered Riemann surfaces does have a real analytic structure but not a complex structure. Is this statement correct? How can I see/prove it?

Any reference (except the papers of Mirzakhani) that studies bordered (ordinary, spin- or super-) Riemann surfaces instead of punctured Riemann surfaces is highly appreciated.

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