John A. Pfaltzgraff’s Home Page

I am a Professor of Mathematics

Education:

• 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.
• Email: jap@math.unc.edu

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

Preprints:

1. Schwarz-Christoffel mapping of multiply connected domains, Journal d`Analyse(with T.K. DeLillo and A.R. Elcrat), accepted June 2003. PDF
2. Schwarz-Christoffel mapping of the annulus, SIAM Review, 43, No. 3 (2001), 469-477 (with T.K. DeLillo and A.R. Elcrat)  PostScript
3. Norm order and geometric properties of holomorphic mappings in C^n Journal D'Analyse Mathematique, 82 (2000), 285-313. (with T.J. Suffridge). PostScript
4. Hyperbolic capacity and its distortion under conformal mapping, Journal D'Analyse Mathematique, 78 (1999), 205-218. (with P.L. Duren). PostScript

Selected Publications:

1. Linear invariance, order and convex maps in C^n (with T. J. Suffridge), Complex Variables. 40 (2000), 35-50.
2. An extension theorem and linear invariant families generated by starlike maps (with T. J. Suffridge), Ann. Univ Mariae Curie-Skl. 53 (1999), 193-207.
3. Distortion of locally biholomorphic maps of the n-ball, Complex Variables Theory Appl. 33 (1997), 239-253.
4. 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.
5. 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).
6. Extremal distance, harmonic measure and numerical conformal mapping, (with T.K. DeLillo), Jour Comp. and Appl. Math. 46 (1993), 103-113.
7. Univalence constraints on the Schwarz-Christoffel parameters, SIAM Jour. of Mathematical Analysis 17 (1986), 231-235.
8. Physical interpretation and further properties of Robin capacity, (with P.L. Duren and R.E. Thurman), Algebra i Analiz 9 (1997), 211-219.
9. Robin capacity and extremal length, Jour. of Mathematical Analysis and Applications 179 (1993), 110-119.
10. Radial symmetrization and capacities in space, Duke Math. J. 34 (1967), 747-756.
11. Subordination chains and quasiconformal extension of holomorphic maps in Cⁿ, Annales Academiae Scientiarum Fennicae 1 (1975), 13-25.
12. Subordination chains and univalence of holomorphic mappings in Cⁿ, Mathematische Annalen 210 (1974), 55-68.
13. Close-to-starlike holomorphic functions of several variables, (with T.J. Suffridge), Pacific Jour. Math. 57 (1975), 271-279.
14. Boundary behavior and linear invariant families, (with D.M. Campbell), Journal D’Analyse Math. 29 (1976).
15. Linear spaces and linear-invariant families of locally univalent functions, (with D.M. Campbell and J.A. Cima), Manuscripta Math. 4 (1971), 1-30.
16. k-Quasiconformal extension criteria in the disk, Complex Variables Theory and Appl. 21 (1993), 293-301.
17. Constrained extremal problems for classes of meromorphic functions, (with B. Pinchuk), Jour. D’Analyse Math. 24 (1971), 101-150.