The Teichmüller space $T_g$ of a closed riemann surface $S_g$ of genus $g \geq 2$ can't be parametrized by $6g-6$ geodesic length functions

convex-analysis hyperbolic-geometry riemann-surfaces teichmueller-theory

Solution 1:

As proposed in the comments, I posted this question on MathOverflow and it got an answer there. Here is the link:

The question on MathOverflow (answered)

Thanks to everyone who read the question and thought about it.

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