## Contact

Email: | neilcourse@gmail.com |

Address: | Okan Üniversitesi Fen-Edebiyat Fakültesi Matematik Bölümü Tuzla Kampüsü 34959 Akfırat-Tuzla İSTANBUL Turkey |

## Research Interests

Topics of interest include: *f*-Harmonic Maps, namely critical points of the energy
functional $E_f(u):=\frac{1}{2} \int_M f |\nabla u|^2 dM$; the associated *L²* flow, which
is called the *f*-Harmonic Heat Flow; Bi-harmonic Maps which may be defined to be
critical points of either $E_e(u):=\frac{1}{2} \int_M |\Delta u|^2 dM$ or
$E_i(u):=\frac{1}{2} \int_M |\tau u|^2 dM$, and the associated flows.

## Articles

*f*-Harmonic Maps- A study of
*f*-harmonic maps and*f*-harmonic heat flow. Topics considered include; the class of*f*-harmonic maps which map the boundary to one point; and locations of singularities under the flow. (Full Abstract)

PhD Thesis, University of Warwick, Coventry, CV4 7AL, UK, 2004.

(Neil_Course_f-harmonic_maps.pdf 935 kB). *f*-harmonic maps which map the boundary of the domain to one point in the target- One considers the class of maps
*u*, from the 2-disc to the 2-sphere, which map the boundary of*D*to one point in*S*. If^{2}*u*were also harmonic, then it is known that*u*must be constant. However, if*u*is instead*f*-harmonic then this need not be true. We see that there exist functions*f: D → (0,∞)*and nonconstant*f*-harmonic maps*u: D → S*which map the boundary to one point. We also see that there exist nonconstant^{2}*f*for which, there is no nonconstant*f*-harmonic map in this class. Finally, we see that there exists a nonconstant*f*-harmonic map from the torus to the 2-sphere.

New York J. Math. 13 (2007) 423-435. (link).