We study harmonic maps from a 3-manifold with boundary to $$\mathbb {S}^1$$ and prove special case of Gromov dihedral rigidity three-dimensional cubes whose angles are $$\pi / 2$$ . Furthermore, we give some applications mapping torus hyperbolic 3-manifolds.

Abstract We consider functions with an asymptotic mean value property, known to characterize harmonicity in Riemannian manifolds and doubling metric measure spaces. show that the strongly amv-harmonic are Hölder continuous for any exponent below one. More generally, we define class of finite amv-norm this belong a fractional Hajłasz–Sobolev space their blow-ups satisfy mean-value property. Furt...

A novel unbiased frequency estimator for a single real-valued sinusoid in white noise is proposed, which is based on a normalized second-order infinite impulse response (IIR) notch filter, and can be seen as an extension of the Pisarenko harmonic decomposer (PHD) estimator. The new estimator inherits the simplicity of the PHD estimator and the high accuracy and selectivity achieved by an IIR fi...