On uniqueness for hyperbolic half-wave maps in dimension d ≥ 3

We obtain a uniqueness result for the half-wave maps equation in dimension d ≥ 3 in the natural energy class with H² target. We first reformulate the half-wave maps equation into a wave maps equation, then isometrically embed H² into some Rᵐ using the Nash embedding, and then use a Gr\"{o}nwall's argument.