Bergman completeness is not a quasi-conformal invariant
Xu Wang
TL;DR
This paper demonstrates that Bergman completeness, a property related to the function theory of Riemann surfaces, is not preserved under quasi-conformal mappings in general cases.
Contribution
It provides a counterexample showing Bergman completeness is not a quasi-conformal invariant for general Riemann surfaces.
Findings
Bergman completeness is not invariant under quasi-conformal maps.
Counterexamples exist for general Riemann surfaces.
The invariance fails beyond special classes of surfaces.
Abstract
We show that Bergman completeness is not a quasi-conformal invariant for general Riemann surfaces.
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Taxonomy
TopicsHolomorphic and Operator Theory · Geometry and complex manifolds · Analytic and geometric function theory