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, E. Poletsky) Amer. J. of Math. 125, 289-299 (2003) .

"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.


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