Harmonic diffeomorphisms, minimizing harmonic maps and rotational symmetry

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Symmetry-selective third-harmonic generation from plasmonic metacrystals.

Nonlinear processes are often governed by selection rules imposed by the symmetries of the molecular configurations. The most well-known examples include the role of centrosymmetry breaking for the generation of even harmonics, and the selection rule related to the rotational symmetry in harmonic generation for fundamental beams with circular polarizations. While the role of centrosymmetry brea...

Locally Minimizing Smooth Harmonic Maps from Asymptotically Flat Manifolds into Spheres

By minimizing the so–called relative energy, we show that there exists a family of locally minimizing smooth harmonic maps from asymptotically flat manifolds into the standard sphere.

High-speed measurement of rotational anisotropy nonlinear optical harmonic generation using position-sensitive detection.

We present a method of performing high-speed rotational anisotropy nonlinear optical harmonic generation experiments at rotational frequencies of several hertz by projecting the harmonic light reflected at different angles from a sample onto a stationary position-sensitive detector. The high rotational speed of the technique, 10(3) to 10(4) times larger than existing methods, permits precise me...

Harmonic Maps and Biharmonic Maps

This is a survey on harmonic maps and biharmonic maps into (1) Riemannian manifolds of non-positive curvature, (2) compact Lie groups or (3) compact symmetric spaces, based mainly on my recent works on these topics.