The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Feng Rong - One of the best experts on this subject based on the ideXlab platform.
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remarks on quasi Reinhardt domains
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2019Co-Authors: Feng RongAbstract:We present some fundamental properties of quasi-Reinhardt domains, in connection with Kobayashi hyperbolicity, minimal domains and representative domains. We also study proper holomorphic correspondences between quasi-Reinhardt domains.
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the degree of biholomorphisms of quasi Reinhardt domains fixing the origin
arXiv: Complex Variables, 2018Co-Authors: Feng RongAbstract:We give a description of biholomorphisms of quasi-Reinhardt domains fixing the origin via Bergman representative coordinates, which are shown to be polynomial mappings with a degree bound given by the so-called "resonance order".
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on biholomorphisms between bounded quasi Reinhardt domains
arXiv: Complex Variables, 2016Co-Authors: Fusheng Deng, Feng RongAbstract:In this paper, we define what is called a quasi-Reinhardt domain and study biholomorphisms between such domains. We show that all biholomorphisms between two bounded quasi-Reinhardt domains fixing the origin are polynomial mappings, and we give a uniform upper bound for the degree of such polynomial mappings. In particular, we generalize the classical Cartan's linearity theorem for circular domains to quasi-Reinhardt domains.
Yunus E Zeytuncu - One of the best experts on this subject based on the ideXlab platform.
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hilbert schmidt hankel operators with anti holomorphic symbols on complete pseudoconvex Reinhardt domains
Czechoslovak Mathematical Journal, 2017Co-Authors: Mehmet Celik, Yunus E ZeytuncuAbstract:On complete pseudoconvex Reinhardt domains in ℂ2, we show that there is no nonzero Hankel operator with anti-holomorphic symbol that is Hilbert-Schmidt. In the proof, we explicitly use the pseudoconvexity property of the domain. We also present two examples of unbounded non-pseudoconvex domains in ℂ2 that admit nonzero Hilbert-Schmidt Hankel operators with anti-holomorphic symbols. In the first example the Bergman space is finite dimensional. However, in the second example the Bergman space is infinite dimensional and the Hankel operator $${H_{{{\bar z}_1}{{\bar z}_2}}}$$ is Hilbert-Schmidt.
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nilpotent toeplitz operators on Reinhardt domains
Rocky Mountain Journal of Mathematics, 2016Co-Authors: Mehmet Celik, Yunus E ZeytuncuAbstract:We construct explicit examples of non-trivial nilpotent Toeplitz operators on Bergman spaces of certain Reinhardt domains in $\mathbb{C}^2$.
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hilbert schmidt hankel operators with anti holomorphic symbols on complete pseudoconvex Reinhardt domains
arXiv: Complex Variables, 2015Co-Authors: Mehmet Celik, Yunus E ZeytuncuAbstract:On complete pseudoconvex Reinhardt domains in $\mathbb{C}^2$, we show that there is no nonzero Hankel operator with an anti-holomorphic symbol that is Hilbert-Schmidt. We also present examples of unbounded non-pseudoconvex domains that admit nonzero Hilbert-Schmidt Hankel operators with anti-holomorphic symbols.
Steven G Krantz - One of the best experts on this subject based on the ideXlab platform.
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automorphism groups and classification of Reinhardt domains
2011Co-Authors: Robert E Greene, Kangtae Kim, Steven G KrantzAbstract:This chapter will give a brief survey of results about the automorphisms of domains that possess circular symmetries. They are a rich source of examples in the study of invariant geometry and automorphism groups.
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on the dimensions of the automorphism groups of hyperbolic Reinhardt domains
arXiv: Complex Variables, 1998Co-Authors: James A Gifford, Alexander Isaev, Steven G KrantzAbstract:We study the possible dimensions that the groups of holomorphic automorphisms of hyperbolic Reinhardt domains can have. We are particularly interested in the problem of characterizing Reinhardt domains with automorphism group of prescribed dimension.
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finite type conditions on Reinhardt domains
Complex Variables and Elliptic Equations, 1996Co-Authors: Alexander Isaev, Steven G KrantzAbstract:We prove that, if ρ is a boundary point of a smoothly bounded pseudoconvex Reinhardt domain in , then the variety type at ρ is identical to the regular type.
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finitely smooth Reinhardt domains with non compact automorphism group
arXiv: Complex Variables, 1996Co-Authors: Alexander Isaev, Steven G KrantzAbstract:We give a complete description of bounded Reinhardt domains of finite boundary smoothness that have non-compact automorphism group. As part of this program, we show that the classification of domains with non-compact automorphism group and having only finite boundary smoothness is considerably more complicated than the classification of such domains that have infinitely smooth boundary.
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Reinhardt domains with non compact automorphism groups
arXiv: Complex Variables, 1995Co-Authors: Alexander Isaev, Steven G KrantzAbstract:We give an explicit description of smoothly bounded Reinhardt domains with noncompact automorphism groups. In particular, this description confirms a special case of a conjecture of Greene/Krantz.
Mehmet Celik - One of the best experts on this subject based on the ideXlab platform.
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hilbert schmidt hankel operators with anti holomorphic symbols on complete pseudoconvex Reinhardt domains
Czechoslovak Mathematical Journal, 2017Co-Authors: Mehmet Celik, Yunus E ZeytuncuAbstract:On complete pseudoconvex Reinhardt domains in ℂ2, we show that there is no nonzero Hankel operator with anti-holomorphic symbol that is Hilbert-Schmidt. In the proof, we explicitly use the pseudoconvexity property of the domain. We also present two examples of unbounded non-pseudoconvex domains in ℂ2 that admit nonzero Hilbert-Schmidt Hankel operators with anti-holomorphic symbols. In the first example the Bergman space is finite dimensional. However, in the second example the Bergman space is infinite dimensional and the Hankel operator $${H_{{{\bar z}_1}{{\bar z}_2}}}$$ is Hilbert-Schmidt.
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nilpotent toeplitz operators on Reinhardt domains
Rocky Mountain Journal of Mathematics, 2016Co-Authors: Mehmet Celik, Yunus E ZeytuncuAbstract:We construct explicit examples of non-trivial nilpotent Toeplitz operators on Bergman spaces of certain Reinhardt domains in $\mathbb{C}^2$.
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hilbert schmidt hankel operators with anti holomorphic symbols on complete pseudoconvex Reinhardt domains
arXiv: Complex Variables, 2015Co-Authors: Mehmet Celik, Yunus E ZeytuncuAbstract:On complete pseudoconvex Reinhardt domains in $\mathbb{C}^2$, we show that there is no nonzero Hankel operator with an anti-holomorphic symbol that is Hilbert-Schmidt. We also present examples of unbounded non-pseudoconvex domains that admit nonzero Hilbert-Schmidt Hankel operators with anti-holomorphic symbols.
Michael J. Mossinghoff - One of the best experts on this subject based on the ideXlab platform.
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Most Reinhardt polygons are sporadic
Geometriae Dedicata, 2019Co-Authors: Kevin G. Hare, Michael J. MossinghoffAbstract:A Reinhardt polygon is a convex n -gon that, for n not a power of 2, is optimal in three different geometric optimization problems, for example, it has maximal perimeter relative to its diameter. Some such polygons exhibit a particular periodic structure; others are termed sporadic . Prior work has described the periodic case completely, and has shown that sporadic Reinhardt polygons occur for all n of the form $$n=pqr$$ n = p q r with p and q distinct odd primes and $$r\ge 2$$ r ≥ 2 . We show that (dihedral equivalence classes of) sporadic Reinhardt polygons outnumber the periodic ones for almost all n , and find that this first occurs at $$n=105$$ n = 105 . We also determine a formula for the number of sporadic Reinhardt polygons when $$n=2pq$$ n = 2 p q with p and q distinct odd primes.
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most Reinhardt polygons are sporadic
arXiv: Metric Geometry, 2014Co-Authors: Kevin G. Hare, Michael J. MossinghoffAbstract:A \textit{Reinhardt polygon} is a convex $n$-gon that, for $n$ not a power of $2$, is optimal in three different geometric optimization problems, for example, it has maximal perimeter relative to its diameter. Some such polygons exhibit a particular periodic structure; others are termed \textit{sporadic}. Prior work has described the periodic case completely, and has shown that sporadic Reinhardt polygons occur for all $n$ of the form $n=pqr$ with $p$ and $q$ distinct odd primes and $r\geq2$. We show that (dihedral equivalence classes of) sporadic Reinhardt polygons outnumber the periodic ones for almost all $n$, and find that this first occurs at $n=105$. We also determine a formula for the number of sporadic Reinhardt polygons when $n=2pq$ with $p$ and $q$ distinct odd primes.
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Sporadic Reinhardt Polygons
Discrete & Computational Geometry, 2013Co-Authors: Kevin G. Hare, Michael J. MossinghoffAbstract:Let $$n$$ be a positive integer, not a power of two. A Reinhardt polygon is a convex $$n$$-gon that is optimal in three different geometric optimization problems: it has maximal perimeter relative to its diameter, maximal width relative to its diameter, and maximal width relative to its perimeter. For almost all $$n$$, there are many Reinhardt polygons with $$n$$ sides, and many of them exhibit a particular periodic structure. While these periodic polygons are well understood, for certain values of $$n$$, additional Reinhardt polygons exist, which do not possess this structured form. We call these polygons sporadic. We completely characterize the integers $$n$$ for which sporadic Reinhardt polygons exist, showing that these polygons occur precisely when $$n=pqr$$ with $$p$$ and $$q$$ distinct odd primes and $$r\ge 2$$. We also prove that a positive proportion of the Reinhardt polygons with $$n$$ sides is sporadic for almost all integers $$n$$, and we investigate the precise number of sporadic Reinhardt polygons that are produced for several values of $$n$$ by a construction that we introduce.
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Sporadic Reinhardt polygons
arXiv: Metric Geometry, 2012Co-Authors: Kevin G. Hare, Michael J. MossinghoffAbstract:Let $n$ be a positive integer, not a power of two. A \textit{Reinhardt polygon} is a convex $n$-gon that is optimal in three different geometric optimization problems: it has maximal perimeter relative to its diameter, maximal width relative to its diameter, and maximal width relative to its perimeter. For almost all $n$, there are many Reinhardt polygons with $n$ sides, and many of them exhibit a particular periodic structure. While these periodic polygons are well understood, for certain values of $n$, additional Reinhardt polygons exist that do not possess this structured form. We call these polygons \textit{sporadic}. We completely characterize the integers $n$ for which sporadic Reinhardt polygons exist, showing that these polygons occur precisely when $n=pqr$ with $p$ and $q$ distinct odd primes and $r\geq2$. We also prove that a positive proportion of the Reinhardt polygons with $n$ sides are sporadic for almost all integers $n$, and we investigate the precise number of sporadic Reinhardt polygons that are produced for several values of $n$ by a construction that we introduce.