On a problem of Bremermann concerning Runge domains

Joiţa, Cezar

doi:10.1007/s00208-006-0041-7

Cited by 4 publications

(4 citation statements)

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“…It is proved in [9] (in [20] for linear case) that any spirallike domain with respect to an asymptotically stable vector field is Runge. But, in view of Joit ¸a [27], this does not imply the closure of the domain, in case the domain is bounded, is polynomially convex. Hamada also provided an example in [21] showing that strictly spirallike is crucial, even in case the vector field is linear.…”

Section: Introduction and Statements Of The Resultsmentioning

confidence: 98%

“…However, in [26,Example 2.7], it was shown that the closure of a bounded strongly pseudoconvex domain with a smooth boundary may not be polynomially convex. In [27], Joit ¸a gave an example of a strongly pseudoconvex domain in C n with real analytic boundary whose closure is not polynomially convex. The doamin in the example of Joit ¸a [27] is a is also a Runge domain.…”

Section: Introduction and Statements Of The Resultsmentioning

confidence: 99%

“…In [27], Joit ¸a gave an example of a strongly pseudoconvex domain in C n with real analytic boundary whose closure is not polynomially convex. The doamin in the example of Joit ¸a [27] is a is also a Runge domain. This raises a natural question: For which classes of pseudoconvex domains the closure is polynomially convex?…”

Section: Introduction and Statements Of The Resultsmentioning

confidence: 99%

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Department of plastic surgery, IPGME&R, Kolkata

Chatterjee

2004

Indian J Plast Surg

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In this paper, we prove that the closure of a bounded pseudoconvex domain, which is spirallike with respect to a globally asymptotic stable holomorphic vector field, is polynomially convex. We also provide a necessary and sufficient condition, in terms of polynomial convexity, on a univalent function defined on a strongly convex domain for embedding it into a filtering Loewner chain. Next, we provide an application of our first result. We show that for any bounded pseudoconvex strictly spirallike domain Ω in C n and given any connected complex manifold Y , there exists a holomorphic map from the unit disc to the space of all holomorphic maps from Ω to Y . This also yields us the existence of O(Ω, Y )-universal map for any generalized translation on Ω, which, in turn, is connected to the hypercyclicity of certain composition operators on the space of manifold valued holomorphic maps.

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Section: Introduction and Statements Of The Resultsmentioning

confidence: 98%

Section: Introduction and Statements Of The Resultsmentioning

confidence: 99%

Section: Introduction and Statements Of The Resultsmentioning

confidence: 99%

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Department of plastic surgery, IPGME&R, Kolkata

Chatterjee

2004

Indian J Plast Surg

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“…Is it true that D is Runge in C n ?". Negative answers to this problem have also recently been given in [1] and [5]. On can infact show, using an argument as above together with the argument principle, that if R is a smoothly bounded planar domain and if ϕ(R) is a holomorphic embedding of R into C 2 with ϕ(∂R) ⊂ , then ϕ(R) ⊂ .…”

Section: Introductionmentioning

confidence: 99%