Fix a Riemannian surface of negative curvature (N, h), and a differentiable surface M g of the same genus g that will host various structures. Also fix a diffeomorphism f0 : M → N . It is well known ([ES], [A], [SY1], [Sa]) that to every complex structure σ on M , there is a unique harmonic diffeomorphism f(σ) : M(σ) → (N, h) homotopic to f0 : M → N ; one is led to consider what other, possibly...

In this paper we establish the higher-dimensional energy bubbling results for harmonic maps to spheres. We have shown in particular that the energy density of concentrations has to be the sum of energies of harmonic maps from the standard 2dimensional spheres. The result also applies to the structure of tangent maps of stationary harmonic maps at either a singularity or infinity. 0. Introductio...

We propose an iterative filterbank method for tracking the parameters of exponentially damped sinusoidal components of quasiharmonic sounds. The quasi-harmonic criteria specialize our analysis to a wide variety of acoustic instrument recordings while allowing for inharmonicity. The filterbank splits the recorded signal into subbands, one per harmonic, in which time-varying parameters of multipl...

In [Hz], Heinz proved that there is no harmonic diffeomorphism from the unit disk D onto the complex plane C. The result was generalized by Schoen [S] and he proved that there is no harmonic diffeomorphism from the unit disk onto a complete surface of nonnegative curvature. Unlike conformal or quasi-conformal maps between Riemann surfaces, the inverse of a harmonic map is not harmonic in genera...

We prove sharp upper and lower bounds for the nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces with boundary. The argument involves frequency function methods for harmonic functions in the interior of the surface as well as the construction of exponentially accurate approximations for the Steklov eigenfunctions near the boundary.

Spherical harmonics have been important tools for solving geophysical and astrophysical problems. Methods have been developed to effectively implement spherical harmonic expansion approximations. However, the Gibbs phenomenon was already observed by Weyl for spherical harmonic expansion approximations to functions with discontinuities, causing undesirable oscillations over the entire sphere. Re...

We show that for planar dispersing billiards the return times distribution is in the limit Poisson for metric balls almost everywhere w.r.t. the SRB measure. Since the Poincaré return map is piecewise smooth but becomes singular at the boundaries of the partition elements, recent results on the limiting distribution of return times cannot be applied as they require the maps to have bounded seco...

The normal Gauss map of a minimal surface in the model space Sol of solvegeometry is a harmonic map with respect to a certain singular Riemannian metric on the extended complex plane.