18 citations · 63 across the 25 of their papers we have counts for
9 papers · 1 filter
Local rigidity for hyperbolic groups with Sierpiński carpet boundaries
Sergei Merenkov
Let and be Kleinian groups whose limit sets and , respectively, are homeomorphic to the standard Sierpiński carpet, and such that every complementary c…
Determining biholomorphic type of a manifold using combinatorial and algebraic structures
Sergei Merenkov
We settle two problems of reconstructing a biholomorphic type of a manifold. In the first problem we use graphs associated to Riemann surfaces of a particular class. In the second…
Local rigidity of Schottky maps
Sergei Merenkov
We introduce Schottky maps-conformal maps between relative Schottky sets, and study their local rigidity properties. This continues the investigations of relative Schottky sets ini…
Equivalence of domains with isomorphic semigroups of endomorphisms
Sergei Merenkov
For two bounded domains in the complex plane whose semigroups of analytic endomorphisms are isomorphic, Eremenko proved in 1993 that the isomorphism is given as a conjugation by a…
On the Cauchy transform of the Bergman space
Sergei Merenkov
The range of the Bergman space B_2(G) under the Cauchy transform K is described for a large class of domains. For a quasidisk G the relation K(B_2^*(G))=B_2^1(\mathbb C\setminus\ba…
On the Cauchy transform of weighted Bergman spaces
Sergei Merenkov
The problem of describing the range of a Bergman space B_2(G) under the Cauchy transform K for a Jordan domain G was solved by Napalkov (Jr) and Yulmukhametov. It turned out that K…