ncts

Since Eells-Sampson in '64, harmonic map flow has been studied widely and provided useful techniques in various fields in geometry. But its understanding is complicated due to the so-called "bubble phenomenon". Recently, there are several attempts to modify domain metric during harmonic map flow. Teichmuller harmonic map flow introduced coupled system of harmonic map flow and evolution of the metric which is L^2 gradient flow of Dirichlet energy. Ricci-harmonic map flow is a combination of harmonic map flow and Ricci flow. And finally conformal heat flow of harmonic maps is a pair of equations of harmonic map flow and conformal evolution of the metric. In this talk, I will present these systems and provide known results. In particular, I will compare them in terms of bubbling and explain how the additional metric change affects the bubble formation.