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.
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.
Stefan Bergman (1977)
Annales Polonici Mathematici
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Väisälä, Jussi (1994)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Avhadiev, F.G., Salahutdinov, R.G. (2001)
Lobachevskii Journal of Mathematics
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McCarthy, John, Papadopoulos, Athanase (1996)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Nikolai Nikolov (2006)
Annales Polonici Mathematici
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We prove that the symmetrized polydisc cannot be exhausted by domains biholomorphic to convex domains.
Ahmed Ayache, Hanen Monceur (2011)
Colloquium Mathematicae
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We investigate the elasticity of atomic domains of the form ℜ = A + XB[X], where X is an indeterminate, A is a local domain that is not a field, and A ⊂ B is a minimal extension of integral domains. We provide the exact value of the elasticity of ℜ in all cases depending the position of the maximal ideals of B. Then we investigate when such domains are half-factorial domains.
Nan Wu, Zu Xing Xuan (2014)
Annales Polonici Mathematici
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We investigate the uniqueness of transcendental algebroid functions with shared values in some angular domains instead of the whole complex plane ℂ. We obtain two theorems which are counterparts of results for meromorphic functions obtained by Zheng.
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...
Karol Borsuk (1972)
Colloquium Mathematicae
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Maciej Skwarczyński
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CONTENTSPRELIMINARY REMARKS........................................................................................ 5 Introduction..................................................................................................... 5 Basic definitions, examples and facts............................................................... 8I. LU QI-KENQ DOMAINS........................................................................................... 13 Some properties of Lu Qi-keng domains.....................................................
Armen Edigarian (2004)
Annales Polonici Mathematici
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We show that the symmetrized bidisc 𝔾₂ = {(λ₁+λ₂,λ₁λ₂):|λ₁|,|λ₂| < 1} ⊂ ℂ² cannot be exhausted by domains biholomorphic to convex domains.
Piermarco Cannarsa, Giuseppe Da Prato, Jean-Paul Zolésio (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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We develolp a new method to solve an evolution equation in a non-cylindrical domain, by reduction to an abstract evolution equation..
Meerschaert, M.M., Scheffler, H.-P. (1996)
Journal of Applied Analysis
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V. Barucci, D.E. Dobbs, M. Fontana (1986)
Manuscripta mathematica
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Nguyen Quang Dieu, Nguyen Thac Dung, Dau Hoang Hung (2005)
Annales Polonici Mathematici
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We study the B-regularity of some classes of domains in ℂⁿ. The results include a complete characterization of B-regularity in the class of Reinhardt domains, we also give some sufficient conditions for Hartogs domains to be B-regular. The last result yields sufficient conditions for preservation of B-regularity under holomorphic mappings.
Klas Diederich, John Erik Fornaess (1978)
Manuscripta mathematica
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Alain Bouvier (1980)
Publications du Département de mathématiques (Lyon)
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Włodzimierz Zwonek
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Our work is divided into five chapters. In Chapter I we introduce necessary notions and we present the most important facts that we shall use. We also present our main results. Chapter I covers the following topics: • holomorphically contractible families of functions and pseudometrics, their basic properties, product property, Lempert Theorem, notion of geodesic, problem of finding effective formulas for invariant functions and pseudometrics and geodesics, completeness...
Peter Pflug, Włodzimierz Zwonek (1998)
Annales Polonici Mathematici
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We find effective formulas for the invariant functions, appearing in the theory of several complex variables, of the elementary Reinhardt domains. This gives us the first example of a large family of domains for which the functions are calculated explicitly.
Sung Woo Choi
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The Minkowski sum of two sets A, B in ℝⁿ is defined to be the set of all points of the form a + b for a ∈ A and b ∈ B. Due to its fundamental nature, the Minkowski sum is an important object in many practical application areas such as image processing, geometric design, robotics, etc. However, compared to the simplicity of the definition, a Minkowski sum of plane domains can have quite complicated topological and geometric features in general. This is the case even when the summands...