Displaying similar documents to “Domains with strong barrier.”

Weak slice conditions, product domains, and quasiconformal mappings.

Stephen M. Buckley, Alexander Stanoyevitch (2001)

Revista Matemática Iberoamericana

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We investigate geometric conditions related to Hölder imbeddings, and show, among other things, that the only bounded Euclidean domains of the form U x V that are quasiconformally equivalent to inner uniform domains are inner uniform domains.

The Carathéodory topology for multiply connected domains II

Mark Comerford (2014)

Open Mathematics

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We continue our exposition concerning the Carathéodory topology for multiply connected domains which we began in [Comerford M., The Carathéodory topology for multiply connected domains I, Cent. Eur. J. Math., 2013, 11(2), 322–340] by introducing the notion of boundedness for a family of pointed domains of the same connectivity. The limit of a convergent sequence of n-connected domains which is bounded in this sense is again n-connected and will satisfy the same bounds. We prove a result...

Generalized John disks

Chang-Yu Guo, Pekka Koskela (2014)

Open Mathematics

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We establish the basic properties of the class of generalized simply connected John domains.

The Carathéodory topology for multiply connected domains I

Mark Comerford (2013)

Open Mathematics

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We consider the convergence of pointed multiply connected domains in the Carathéodory topology. Behaviour in the limit is largely determined by the properties of the simple closed hyperbolic geodesics which separate components of the complement. Of particular importance are those whose hyperbolic length is as short as possible which we call meridians of the domain. We prove continuity results on convergence of such geodesics for sequences of pointed hyperbolic domains which converge...

On nonisometric isospectral connected fractal domains.

Brian D. Sleeman, Chen Hua (2000)

Revista Matemática Iberoamericana

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A fundamental question raised by M. Kac in 1966 is: Must two isospectral planar domains necessarily be isometric? Following a long history of investigation C. Gordon, D. L. Webb and S. Wolpert in 1992 finally proved that the answer is no. By using the idea of transposition maps one can construct a wide class of planar domains with piecewise continuous boundaries which are isospectral but non-isometric. In this note we study the Kac question in relation to domains with fractal boundaries...

Boundary behavior of subharmonic functions in nontangential accessible domains

Shiying Zhao (1994)

Studia Mathematica

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The following results concerning boundary behavior of subharmonic functions in the unit ball of ℝ n are generalized to nontangential accessible domains in the sense of Jerison and Kenig [7]: (i) The classical theorem of Littlewood on the radial limits. (ii) Ziomek’s theorem on the L p -nontangential limits. (iii) The localized version of the above two results and nontangential limits of Green potentials under a certain nontangential condition.

Bounce trajectories in plane tubular domains

Roberto Peirone (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We state that in opportune tubular domains any two points are connected by a bounce trajectory and that there exist non-trivial periodic bounce trajectories.

Bounce trajectories in plane tubular domains

Roberto Peirone (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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We state that in opportune tubular domains any two points are connected by a bounce trajectory and that there exist non-trivial periodic bounce trajectories.