[Math] Conformal Welding Reference

complex-geometryconformal-geometryreference-requestriemann-surfaces

I'm looking for a reference for the following fact: given two Riemann surfaces and an identification of their boundaries, once I topologically glue the surfaces together there exists a unique conformal structure on my new surface that is compatible with the conformal structures I started with.

Best Answer

See MR1966191 (2005e:30012) Hamilton, D. H.(1-MD) Conformal welding. Handbook of complex analysis: geometric function theory, Vol. 1, 137–146, North-Holland, Amsterdam, 2002. 30C35

and other papers by David Hamilton.

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