Introduction to complex dynamics in one dimension
These are notes from elementary lectures given in the summer of 2013 at the YMSC center at Tsinghua University in Beijing.
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arXiv subjects
John Erik Fornæss
Publications and source records attributed to John Erik Fornæss.
A domain with non-plurisubharmonic squeezing function
We construct a strictly pseudoconvex domain with smooth boundary whose squeezing function is not plurisubharmonic.
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A global approximation result by Al Taylor and the strong openness conjecture in C^n
We improve a global approximation result by Al Taylor in C^n for holomorphic functions in weighted Hilbert spaces. The main tools are a variation of the theorem of Hormander on weighted L^2-estimates for the dbar-equation together with the solution of the strong openness conjecture. A counterexample to a global strong openness conjecture in Cn is also given here.
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A characterization of the ball
We study bounded domains with certain smoothness conditions and the properties of their squeezing functions in order to prove that the domains are biholomorphic to the ball.
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On a conjecture by Blocki-Zwonek
The article provides a counterexample to a conjecture by Blocki-Zwonek.
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A survey on non-autonomous basins in several complex variables
Consider a holomorphic automorphism which acts hyperbolically on some invariant compact set. Then for every point in the compact set there exists a stable manifold, which is a complex manifold diffeomorphic to real Euclidean space. If the point is fixed, then the stable manifold is even biholomorphic to complex Euclidean space. In fact, it is known that the stable manifold of a generic point is biholomorphic to Euclidean space, and it has been conjectured that this holds for every point. In this article we survey the history of this problem, addressing both known results and the techniques used to obtain those results. Moreover, we present a list of seemingly simpler open problems and prove several new results, all pointing towards a positive answer to the conjecture discussed above.
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