Harmonic and Wave Maps Coupled with Einstein’s Gravitation

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.

Stable Exponentially Harmonic Maps Between Finsler Manifolds

stable exponentially harmonic maps between finsler manifolds

Self-similar spherically symmetric wave maps coupled to gravity

We investigate spherically symmetric continuously self-similar (CSS) solutions in the SU(2) sigma model coupled to gravity. Using mixed numerical and analytical methods, we provide evidence for the existence (for small coupling) of a countable family of regular CSS solutions. This fact is argued to have important implications for the ongoing studies of black hole formation in the model.

Periodic self-similar wave maps coupled to gravity

We continue our studies of spherically symmetric self-similar solutions in the SU(2) sigma model coupled to gravity. Using mixed numerical and analytical methods we show existence of an unstable periodic solution lying at the boundary between the basins of two generic attractors.