Target Geometry in Prescribed-Value Schwarz Lemmas for Harmonic Maps
We study harmonic maps \(F:\D\to G\) into bounded domains in real Hilbert spaces, prescribing \(F(0)\) and \(dF_0(\R^2)\) when \(dF_0\) is nonzero and conformal. We prove a target-independent identity for the M\"obius-weighted Hilbert pairing. After normalization, the pairing is affine in \(\|dF_0\|\) with positive slo...