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On an extremal problem for harmonic maps conformal at a point
Let \(\mathbb D\) denote the unit disc in \(\mathbb C\). For a domain \(D\subset\mathbb C\) and a point \(p\in D\), let \(M_D(p)\) denote the supremum of \(\|df_0\|\) over all harmonic maps \(f:\mathbb D\to D\) with \(f(0)=p\) whose differential \(df_0\) at \(0\in \mathbb D\) is conformal. If \(f:\m
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