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Some remarks on the Kobayashi–Fuks metric on strongly pseudoconvex domains
Journal of Mathematical Analysis and Applications, 2022 23 ...
Diganta Borah, Debaprasanna Kar
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The automorphism groups of strongly pseudoconvex domains
Mathematische Annalen, 1982 Let \(D_ 0\) be a \(C^{\infty}\) strongly pseudoconvex bounded domain in \({\mathbb{C}}^ n\) (or in a Stein manifold). The authors study the holomorphic automorphism groups Aut(D) of like domains that are \(C^{\infty}\) close to \(D_ 0\). Their main results are as follows: If D is sufficiently \(C^{\infty}\) close to \(D_ 0\), then Aut(D) is isomorphic
Krantz, Steven G., Greene, Robert E.
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Special Toeplitz operators on strongly pseudoconvex domains
Revista Matemática Iberoamericana, 2006 Toeplitz operators on strongly pseudoconvex domains in \mathbb{C}^n , constructed from the Bergman projection and with symbol equal to a positive power of the distance to the boundary, are considered. The mapping properties of these operators on
Čučković , Željko +1 more
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Smooth equivalence of families of strongly pseudoconvex domains
, 2023 We establish a smoothness result for families of biholomorphisms between smooth families of strongly pseudoconvex domains, each with trivial biholomorphism group. This is accomplished by considering the Riemannian geometry of their Bergman metrics and proving a result about the smoothness of families of isometries between smooth families of Riemannian ...
Gaussier, Hervé +2 more
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A Gehring–Hayman Inequality for Strongly Pseudoconvex Domains
International Mathematics Research NoticesAbstract We prove that if $D$ is a strongly pseudoconvex domain with $\mathcal C^{2, \alpha }$-smooth boundary, then the length of a geodesic for the Kobayashi–Royden infinitesimal metric between two points is bounded by a constant multiple of the Euclidean distance between the points.
Kosiński, Łukasz +2 more
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The Carath�odory distance in strongly pseudoconvex domains
Mathematische Annalen, 1994 Let \(G \Subset \mathbb{C}^ n\) be a strongly pseudoconvex domain and \(P_ 0\), \(Q_ 0 \in \partial G\). It is proved that there is a continuous double peak function \(f\) in \(G\) at \(P_ 0\), \(Q_ 0\), i.e., there exist a domain \(G' \Supset G\), two neighbourhoods \(U_ 1,U_ 2\) of \(P_ 0\) and \(Q_ 0\) respectively such that \(f:B_{U_ 1} \times B_ ...
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Fiberwise Kähler-Ricci flows on families of bounded strongly pseudoconvex domains
Documenta Mathematica, 2022 Let \pi:\mathbb{C}^n\times\mathbb{C}\rightarrow \mathbb{C} be the projection map onto the second factor and let D be a domain in
Choi, Young-Jun, Yoo, Sungmin
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Interpolating sequences for weighted Bergman spaces on strongly pseudoconvex bounded domains [PDF]
International Journal of Mathematics, 2021 Let [Formula: see text], [Formula: see text], and [Formula: see text] be a strongly pseudoconvex bounded domain with a smooth boundary in [Formula: see text]. We will study the interpolation problem for weighted Bergman spaces [Formula: see text]. In the case, [Formula: see text], and [Formula: see text], where [Formula: see text] is the conjugate ...
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Condition R and proper holomorphic maps between equidimensional product domains
, 2013 We consider proper holomorphic mappings of equidimensional pseudoconvex domains in complex Euclidean space, where both source and target can be represented as Cartesian products of smoothly bounded domains.
Chakrabarti, Debraj, Verma, Kaushal
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Solutions to $ar{partial}$-equations on strongly pseudo-convex domains with $L^p$-estimates
Electronic Journal of Differential Equations, 2004 We construct a solution to the $ar{partial}$-equation on a strongly pseudo-convex domain of a complex manifold. This is done for forms of type $(0,s)$, $sgeq 1 $, with values in a holomorphic vector bundle which is Nakano positive and for complex valued ...
Osama Abdelkader, Shaban Khidr
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