John A. Pfaltzgraff’s Home Page
I am a Professor of Mathematics
A.B. Harvard 1958
M.S. University of Kentucky 1961
Ph.D. University of Kentucky 1963 (Adviser: W.C. Royster)
How to find me:
Office: 308 Phillips Hall. Office phone: (919) 962-9602.
My research interests:
I am working on problems in: (i) Geometric function theory of one and
several complex variables with a current emphasis on developing a theory
of linear invariance and linear invariant families of biholomorphic mappings
in several variables. (ii) Numerical conformal mapping with current focus
on methods for multiply connected domains and applications. (iii) Robin
capacity and applications. (iv) Plane harmonic mappings. I am directing
Beth Schaubroeck’s Ph.D. dissertation research on plane harmonic mappings.
I am a member of the AMS, SIAM and IMACS
Schwarz-Christoffel mapping of multiply connected domains, Journal d`Analyse(with
T.K. DeLillo and A.R. Elcrat), accepted June 2003. PDF
Schwarz-Christoffel mapping of the annulus, SIAM Review, 43, No. 3 (2001),
469-477 (with T.K. DeLillo and A.R. Elcrat) PostScript
Norm order and geometric properties of holomorphic mappings in C^n Journal
D'Analyse Mathematique, 82 (2000), 285-313. (with T.J. Suffridge). PostScript
Hyperbolic capacity and its distortion under conformal mapping, Journal
D'Analyse Mathematique, 78 (1999), 205-218. (with P.L. Duren). PostScript
Linear invariance, order and convex maps in C^n (with T. J. Suffridge),
Complex Variables. 40 (2000), 35-50.
An extension theorem and linear invariant families generated by starlike
maps (with T. J. Suffridge), Ann. Univ Mariae Curie-Skl. 53 (1999), 193-207.
Distortion of locally biholomorphic maps of the n-ball, Complex Variables
Theory Appl. 33 (1997), 239-253.
Numerical conformal mapping methods based on Faber series, (with T.K. DeLillo
and A.R. Elcrat), Jour. Computational and Appl. Math. 83 (1997), 205-236.
Numerical conformal mapping methods for simply and doubly connected regions,
(with T.K. DeLillo), to appear in SIAM Jour. on Scientific Computing, special
issue on iterative methods, (Jan. 1998).
Extremal distance, harmonic measure and numerical conformal mapping, (with
T.K. DeLillo), Jour Comp. and Appl. Math. 46 (1993), 103-113.
Univalence constraints on the Schwarz-Christoffel parameters, SIAM Jour.
of Mathematical Analysis 17 (1986), 231-235.
Physical interpretation and further properties of Robin capacity, (with
P.L. Duren and R.E. Thurman), Algebra i Analiz 9 (1997), 211-219.
Robin capacity and extremal length, Jour. of Mathematical Analysis and
Applications 179 (1993), 110-119.
Radial symmetrization and capacities in space, Duke Math. J. 34 (1967),
Subordination chains and quasiconformal extension of holomorphic maps in
Cn, Annales Academiae Scientiarum Fennicae 1 (1975), 13-25.
Subordination chains and univalence of holomorphic mappings in Cn,
Mathematische Annalen 210 (1974), 55-68.
Close-to-starlike holomorphic functions of several variables, (with T.J.
Suffridge), Pacific Jour. Math. 57 (1975), 271-279.
Boundary behavior and linear invariant families, (with D.M. Campbell),
Journal D’Analyse Math. 29 (1976).
Linear spaces and linear-invariant families of locally univalent functions,
(with D.M. Campbell and J.A. Cima), Manuscripta Math. 4 (1971), 1-30.
k-Quasiconformal extension criteria in the disk, Complex Variables Theory
and Appl. 21 (1993), 293-301.
Constrained extremal problems for classes of meromorphic functions, (with
B. Pinchuk), Jour. D’Analyse Math. 24 (1971), 101-150.