Harmonic Maps and Their Applications in Surface Matching

Gravity acceleration at the sea surface derived from satellite altimetry data using harmonic splines

Gravity acceleration data have grand pursuit for marine applications. Due to environmental effects, marine gravity observations always hold a high noise level. In this paper, we propose an approach to produce marine gravity data using satellite altimetry, high-resolution geopotential models and harmonic splines. On the one hand, harmonic spline functions have great capability for local gravity ...

Harmonic Flow for Histogram Matching

We present a method to perform histogram matching between two color images based on the concept of harmonic mapping between Riemannian manifolds. The key idea is to associate the histogram of a color image to a Riemannian manifold. In this context, the energy of the matching between the two images is measured by the Dirichlet energy of the mapping between the Riemannian manifolds. Then, we assi...

Applications of non-collinear second harmonic generation in one-dimensional periodically poled crystals

Whereas the commonly used collinear quasi-phase-matched interaction is usually suitable for phase matching only a single nonlinear process, non-collinear interactions offer rich variety of phase matching possibilities, employing different elements of the nonlinear tensor, and various orders of quasi phase matching. By studying the dependence of the second harmonic process on the angle and the p...

From Stochastic Parallel Transport to Harmonic Maps Dirichlet Forms and Their Applications in Geometry and Stochastics from Stochastic Parallel Transport to Harmonic Maps

S ep 2 00 9 ALL HARMONIC 2 - SPHERES IN THE UNITARY GROUP , COMPLETELY EXPLICITLY

We give a completely explicit formula for all harmonic maps of finite uniton number from a Riemann surface to the unitary group U(n) in any dimension, and so all harmonic maps from the 2-sphere, in terms of freely chosen meromorphic functions on the surface and their derivatives, using only combinations of projections and avoiding the usual ∂-problems or loop group factorizations. We interpret ...