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If it turns out that a problem is equivalent to a known open problem, then the open-problem tag is added. After that, the question essentially becomes, "What is known about this problem? What are some possible ways to approach this problem? What are some ways that people have tried to attack it before, and with what results?"

4 votes

Midpoint geodesic polygon / Birkhoff curve shortening

You may also have a look at the paper https://arxiv.org/pdf/1502.01741.pdf
Tony Lelievre's user avatar