= Reich–Strebel inequality
{c}
{title2=$K_0\leq\int_X\frac{|1+\mu_fq/|q||^2}{1-|\mu_f|^2}|q|$}
On closed <Riemann surfaces> of <genus> at least two, if a <Teichmüller map> $f_0:X\to Y$ has unit-area source differential $q$ and dilatation $K_0$, any <quasiconformal map> $f:X\to Y$ in the same <homotopy class> satisfies $K_0\leq\int_X|q|\,|1+\mu_fq/|q||^2/(1-|\mu_f|^2)$. The plus sign corresponds to a <Teichmüller map> with $\mu_{f_0}=k_0|q|/q$ and $K_0=(1+k_0)/(1-k_0)$. This fundamental inequality yields <Teichmüller's uniqueness theorem> by the pointwise <triangle inequality> and its equality case. See https://userhome.brooklyn.cuny.edu/gardiner/A%20short%20course%20on%20Teichmuller%27s%20theorem.pdf[Gardiner and Hu, §5, equation (11)].
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