Ngin-Tee Koh

Department of Mathematics
Morton Hall 321
1 Ohio University
Athens, OH 45701

Office: 581 Morton Hall
Phone: (740) 593-1290
Fax: (740) 593-9805
Email: nkoh@syr.edu

Background

Ngin-Tee Koh is a Visiting Assistant Professor at Ohio University. He received his doctorate from the University of Illinois at Urbana-Champaign (UIUC) in 2009. His thesis advisor was Professor Aimo Hinkkanen.

For more details, here's a CV.

Teaching

MAT 397 M005, Spring 2011
MAT 485 M003, Spring 2011
MAT 286 M001, Fall 2010
MAT 286 M002, Fall 2010
MAT 397 M002, Spring 2010
MAT 485 M004, Spring 2010
MAT 397 M003, Fall 2009
MAT 397 M005, Fall 2009

Prior Teaching at UIUC

Math 225 Introductory Matrix Theory, Fall 2008
Math 234 Calculus for Business I, Spring 2007
Math 231 Calculus II, Fall 2006
Math 230 Calculus II, Spring 2006 & Fall 2005
Math 220 Calculus I, Spring 2005 & Fall 2004

Research Specialization

Primary interests include geometric function theory, harmonic mappings, quasiconformal mappings and quasidisks.
Secondary interests include complex dynamics, geometric measure theory, summability methods, Tauberian theory and value distribution theory.

Research Publications & Preprints

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.

Invited Presentations

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.

Mathematical Animations

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. I was introduced to this software by Professor George Francis.