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This is probably a classic problem, so a good reference book or paper to get me started on this type of question would be great: Let $\mathbb{D} \subset \mathbb{C}$ be the unit disk with boundary $\...

I'll state the theorem I am posing up front, and then explain why I think this theorem appears to be true. I am asking if anyone can prove it, or knows references to where it is proved. Please, ...