**Department of Mathematics and Statistics**, **University of Canterbury**.

Ngin-Tee Koh received his doctorate from the University of Illinois at Urbana-Champaign in 2009. His thesis supervisor was Professor Aimo Hinkkanen.

For more details, here's a CV.

- Complex analysis including (but not confined to) conformal mappings, energy-minimal diffeomorphisms, geometric function theory, harmonic mappings, quasiconformal mappings and quasidisks.

Note: Energy-minimal diffeomorphisms are also known as least squares conformal mappings in computer graphics. Their applications include automatic texture atlas generation and geometrically aware and self-configuring projectors.

If you've problems accessing the links below and would like a copy/preprint of any paper, just send me an email.

- Existence of energy-minimal diffeomorphisms between doubly connected domains (with Tadeusz Iwaniec, Leonid Kovalev, and Jani Onninen).
*Invent. Math.*186 (2011), no. 3, 667--707**Abstract:**The paper establishes the existence of homeomorphisms between two planar domains that minimize the Dirichlet energy. Specifically, among all homeomorphisms f : R -> R* between bounded doubly connected domains such that Mod (R) < Mod (R*) there exists, unique up to conformal authomorphisms of R, an energy-minimal diffeomorphism. No boundary conditions are imposed on f. Although any energy-minimal diffeomorphism is harmonic, our results underline the major difference between the existence of harmonic diffeomorphisms and the existence of the energy-minimal diffeomorphisms. The existence of globally invertible energy-minimal mappings is of primary pursuit in the mathematical models of nonlinear elasticity and is also of interest in computer graphics. - Lacunary series and Tauberian-type hypotheses.
*Arch. Math. (Basel)*97 (2011), no. 2, 179-186**Abstract:**In this article, we introduce some Tauberian-type conditions and prove variants of Hardy-Littlewood's high indices theorem for certain classes of series. - Area contraction for harmonic automorphisms of the disk (with Leonid Kovalev).
*Bull. London Math. Soc.*43 (2011), no. 1, 91-96**Abstract:**A harmonic self-homeomorphism of a disk does not increase the area of any concentric disk. - On conformal mappings onto quasidisks.
*Comput. Methods Funct. Theory*10 (2010), no. 1, 215-221**Abstract:**We prove a distortion theorem for conformal mappings whose images are quasidisks. As an application, we construct a quasiconformal reflection with bounded partial derivatives near the reflection boundary based on the Douady-Earle extension. - Approximable quasidisks.
*Ann. Acad. Sci. Fenn. Math.*34 (2009), no. 2, 545-553**Abstract:**We study a question posed by Anderson and Hinkkanen: what quasidisks are approximable? We show that a Jordan domain bounded by an analytic curve is an approximable quasidisk. - Some estimates for normalized quasiconformal self-mappings of the unit disk.
*Complex Var. Elliptic Equ.*54 (2009), no. 5, 425-428**Abstract:**We provide an integral estimate for the boundary values of a normalized quasiconformal self-mapping of the unit disk. Estimates are also given for the partial derivative of the Douady-Earle extension.

- Mathematics and Statistics Seminar, Christchurch, New Zealand, June 2012.
- AMS Meeting: Special Session on Nonlinear Analysis and Geometry, Syracuse, NY, October 2010.
- Conference on Complex Analysis, Urbana, IL, May 2010.
- Analysis Seminar, Syracuse, NY, September 2009.
- AMS Meeting: Special Session on Complex Dynamics and Value Distribution, Urbana, IL, March 2009.
- AMS-MAA Joint National Meetings: Special Session on Complex Dynamics and Complex Function Theory, Washington, D.C., January 2009.

Click on the images below to view the 3D shadows of some rotating 4D surfaces. You'll need the free DPGraph Viewer to see the animations.

Pictures of a Pacific Northwest journey (High speed connection required - if you've a slow connection, you may view the pictures here)