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 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 S2. If 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 → S2 which map the boundary to one point. We also see that there exist nonconstant 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).

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