Research interests and publications
Buma
Fridman
My interests in the past few years have been in the theory of holomorphic functions of several complex variables and analytical geometry.
Specifically: boundary behavior of analytic maps, holomorphic automorphism groups of hyperbolic manifolds, fixed point theorems.
Following is a list of some of my publications.
"On a Class of Analytic Polyhedra''
- Dokl Akad Nauk USSR Vol. 242, No. 5, (1978). Translated in Soviet
Math. Dokl Vol. 19, No. 5, pp. 1258-1261, (1979).
"Biholomorphic Invariants of a Hyperbolic Manifold and
some Applications'', Transactions of the American Math Society, Vol. 276, No.
2, pp. 685-698, (1983).
"One Example of the Boundary Behavior of Biholomorphic
Transformations", Proceedings of the American Math. Society, Vol. 89, No.
2, pp. 226-228, (1983).
"An
Approximate Riemann Mapping Theorem", Mathematische
Annalen, 275, pp. 49-55 (1986).
"A Universal Exhausting Domain'', Proceedings of the
American Math. Society, Vol. 98, No. 2, pp. 267-270, (1986).
"Upper
semicontinuity of automorphism groups" (with
E.A. Poletsky), Mathematische
Annalen, 299, pp. 615-628 (1994).
"A Uniqueness result for a generalized Radon
transform", SIAM Journal of Mathematical Analysis, vol. 26, 6, pp.
1467-1472 (1995). 
"A compact set with noncompact disc-hull " (with
Lop-Hing Ho; Daowei Ma) Proc. Amer. Math. Soc.129, No5, 1473-1475 (2001).
"On fixed points and determining sets for holomorphic
automorphisms" (with K. T. Kim, S. G. Krantz, D. Ma), Michigan Math J, 50,
507-515, (2002).
"Perturbations of Domains and Automorphism
Groups" (with D. Ma), Journal of the Korean Mathematical Society, vol. 40
(3), 487-502 (2003) .
"Upper semicontinuity of the
dimensions of automorphism groups of domains in C^n"
(with D. Ma,
"On determining sets for holomorphic automorphisms"
(with K. T. Kim, S. G. Krantz, D. Ma), Rocky
Mountain Journal of Mathematics, vol. 36, 3 (2006), 947-956.
"Isolated
fixed point sets for holomorphic maps",
(with D. Ma, J-P Vigue), J.
Math. Pures. Appl. 86 (2006), 80-87.
"Properties of Fixed Point Sets and a
Characterization of the Ball in C^n", (with D. Ma), Proc.
Amer. Math. Soc. 135 (2007) 229-236.
"Fixed Points and Determining Sets for Holomorphic
Self-Maps of a Hyperbolic Manifold" (with D. Ma, J-P Vigue),
Michigan Math J, 55
(2007), 229-238.
"Osgood-Hartogs-type Properties of Power Series
and Smooth Functions" (with D. Ma), Pacific J. Math., vol. 251, No. 1
(2011), 67-79.
"Testing holomorphy
on curves"(with D. Ma), Israel J. Math.,
vol. 192 (2012), 535-540.
"Nonlinear convergence sets of divergent power
series" (with D. Ma, T. Neelon),
Annales Polonici Mathematici,
106 (2012), 193-198 
"Holomorphic functions on subsets of C" (with D. Ma), J. Math. Soc. Japan, vol.
65 (2013), 1-12.
Biholomorphic
transformations (with D. Ma). Handbook of
complex analysis, (2022), CRC Press,
Boca Raton, FL, 61–88,.