The Experts below are selected from a list of 327 Experts worldwide ranked by ideXlab platform
Xiangyu Zhou - One of the best experts on this subject based on the ideXlab platform.
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An Extension Theorem with optimal estimate
Comptes Rendus Mathematique, 2014Co-Authors: Qiʼan Guan, Xiangyu ZhouAbstract:Abstract In this note, we establish an L 2 Extension Theorem with an optimal estimate for semi-positive vector bundles in the sense of Nakano. This result also implies optimal estimate versions of various L 2 Extension Theorems. Applications include a solution of the equality case in a conjecture of Suita on logarithmic capacities of open Riemann surface, as well as a solution of the extended Suita conjecture and a confirmation of the so-called L -conjecture.
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Generalized Extension Theorem and a conjecture of Ohsawa
Comptes Rendus Mathematique, 2013Co-Authors: Qiʼan Guan, Xiangyu ZhouAbstract:Abstract In this paper, we determine the optimal constant in the estimate of Ohsawaʼs generalized L 2 Extension Theorem. The result holds for holomorphic vector bundles on a class of complex manifolds including both Stein manifolds and complex projective algebraic manifolds. As an application, we obtain a solution to a related conjecture of Ohsawa.
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optimal constant problem in the l2 Extension Theorem
Comptes Rendus Mathematique, 2012Co-Authors: Qiʼan Guan, Xiangyu ZhouAbstract:Abstract In this Note, we solve the optimal constant problem in the L 2 -Extension Theorem with negligible weight on Stein manifolds. As an application, we prove the Suita conjecture on arbitrary open Riemann surfaces.
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on the ohsawa takegoshi l2 Extension Theorem and the bochner kodaira identity with non smooth twist factor
Journal de Mathématiques Pures et Appliquées, 2012Co-Authors: Langfeng Zhu, Qiʼan Guan, Xiangyu ZhouAbstract:Abstract In this paper, we give detailed proofs of results announced in a previously published note. We improve the estimate in Ohsawaʼs generalization of the Ohsawa–Takegoshi L 2 Extension Theorem by finding a smaller constant, and apply the result to the Suita conjecture. We give and prove a simpler version generalizing the Ohsawa–Takegoshi L 2 Extension Theorem for holomorphic functions to an L 2 Extension Theorem for ∂ ¯ -closed smooth ( n − 1 , q ) -forms. Finally, we prove that the twist factor in the twisted Bochner–Kodaira identity can be a non-smooth plurisuperharmonic function.
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on the ohsawa takegoshi Extension Theorem and the twisted bochner kodaira identity
Comptes Rendus Mathematique, 2011Co-Authors: Qiʼan Guan, Xiangyu Zhou, Langfeng ZhuAbstract:Abstract In this Note, we improve the estimate in Ohsawaʼs generalization of the Ohsawa–Takegoshi L 2 Extension Theorem for holomorphic functions by finding a smaller constant, and apply the result to the Suita conjecture. We also present a remark allowing to generalize the Ohsawa–Takegoshi Extension Theorem to the case of ∂ ¯ -closed smooth ( n − 1 , q ) -forms. Finally, we prove that the twist factor in the twisted Bochner–Kodaira identity can be a non-smooth plurisuperharmonic function.
Zbigniew Blocki - One of the best experts on this subject based on the ideXlab platform.
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suita conjecture and the ohsawa takegoshi Extension Theorem
Inventiones Mathematicae, 2013Co-Authors: Zbigniew BlockiAbstract:We prove a conjecture of N. Suita which says that for any bounded domain D in ℂ one has \(c_{D}^{2}\leq\pi K_{D}\), where cD(z) is the logarithmic capacity of ℂ∖D with respect to z∈D and KD the Bergman kernel on the diagonal. We also obtain optimal constant in the Ohsawa-Takegoshi Extension Theorem.
Qiʼan Guan - One of the best experts on this subject based on the ideXlab platform.
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An Extension Theorem with optimal estimate
Comptes Rendus Mathematique, 2014Co-Authors: Qiʼan Guan, Xiangyu ZhouAbstract:Abstract In this note, we establish an L 2 Extension Theorem with an optimal estimate for semi-positive vector bundles in the sense of Nakano. This result also implies optimal estimate versions of various L 2 Extension Theorems. Applications include a solution of the equality case in a conjecture of Suita on logarithmic capacities of open Riemann surface, as well as a solution of the extended Suita conjecture and a confirmation of the so-called L -conjecture.
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Generalized Extension Theorem and a conjecture of Ohsawa
Comptes Rendus Mathematique, 2013Co-Authors: Qiʼan Guan, Xiangyu ZhouAbstract:Abstract In this paper, we determine the optimal constant in the estimate of Ohsawaʼs generalized L 2 Extension Theorem. The result holds for holomorphic vector bundles on a class of complex manifolds including both Stein manifolds and complex projective algebraic manifolds. As an application, we obtain a solution to a related conjecture of Ohsawa.
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optimal constant problem in the l2 Extension Theorem
Comptes Rendus Mathematique, 2012Co-Authors: Qiʼan Guan, Xiangyu ZhouAbstract:Abstract In this Note, we solve the optimal constant problem in the L 2 -Extension Theorem with negligible weight on Stein manifolds. As an application, we prove the Suita conjecture on arbitrary open Riemann surfaces.
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on the ohsawa takegoshi l2 Extension Theorem and the bochner kodaira identity with non smooth twist factor
Journal de Mathématiques Pures et Appliquées, 2012Co-Authors: Langfeng Zhu, Qiʼan Guan, Xiangyu ZhouAbstract:Abstract In this paper, we give detailed proofs of results announced in a previously published note. We improve the estimate in Ohsawaʼs generalization of the Ohsawa–Takegoshi L 2 Extension Theorem by finding a smaller constant, and apply the result to the Suita conjecture. We give and prove a simpler version generalizing the Ohsawa–Takegoshi L 2 Extension Theorem for holomorphic functions to an L 2 Extension Theorem for ∂ ¯ -closed smooth ( n − 1 , q ) -forms. Finally, we prove that the twist factor in the twisted Bochner–Kodaira identity can be a non-smooth plurisuperharmonic function.
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on the ohsawa takegoshi Extension Theorem and the twisted bochner kodaira identity
Comptes Rendus Mathematique, 2011Co-Authors: Qiʼan Guan, Xiangyu Zhou, Langfeng ZhuAbstract:Abstract In this Note, we improve the estimate in Ohsawaʼs generalization of the Ohsawa–Takegoshi L 2 Extension Theorem for holomorphic functions by finding a smaller constant, and apply the result to the Suita conjecture. We also present a remark allowing to generalize the Ohsawa–Takegoshi Extension Theorem to the case of ∂ ¯ -closed smooth ( n − 1 , q ) -forms. Finally, we prove that the twist factor in the twisted Bochner–Kodaira identity can be a non-smooth plurisuperharmonic function.
Langfeng Zhu - One of the best experts on this subject based on the ideXlab platform.
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on the ohsawa takegoshi l2 Extension Theorem and the bochner kodaira identity with non smooth twist factor
Journal de Mathématiques Pures et Appliquées, 2012Co-Authors: Langfeng Zhu, Qiʼan Guan, Xiangyu ZhouAbstract:Abstract In this paper, we give detailed proofs of results announced in a previously published note. We improve the estimate in Ohsawaʼs generalization of the Ohsawa–Takegoshi L 2 Extension Theorem by finding a smaller constant, and apply the result to the Suita conjecture. We give and prove a simpler version generalizing the Ohsawa–Takegoshi L 2 Extension Theorem for holomorphic functions to an L 2 Extension Theorem for ∂ ¯ -closed smooth ( n − 1 , q ) -forms. Finally, we prove that the twist factor in the twisted Bochner–Kodaira identity can be a non-smooth plurisuperharmonic function.
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on the ohsawa takegoshi Extension Theorem and the twisted bochner kodaira identity
Comptes Rendus Mathematique, 2011Co-Authors: Qiʼan Guan, Xiangyu Zhou, Langfeng ZhuAbstract:Abstract In this Note, we improve the estimate in Ohsawaʼs generalization of the Ohsawa–Takegoshi L 2 Extension Theorem for holomorphic functions by finding a smaller constant, and apply the result to the Suita conjecture. We also present a remark allowing to generalize the Ohsawa–Takegoshi Extension Theorem to the case of ∂ ¯ -closed smooth ( n − 1 , q ) -forms. Finally, we prove that the twist factor in the twisted Bochner–Kodaira identity can be a non-smooth plurisuperharmonic function.
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On the Ohsawa–Takegoshi Extension Theorem and the twisted Bochner–Kodaira identity
Comptes Rendus Mathematique, 2011Co-Authors: Qiʼan Guan, Xiangyu Zhou, Langfeng ZhuAbstract:Abstract In this Note, we improve the estimate in Ohsawaʼs generalization of the Ohsawa–Takegoshi L 2 Extension Theorem for holomorphic functions by finding a smaller constant, and apply the result to the Suita conjecture. We also present a remark allowing to generalize the Ohsawa–Takegoshi Extension Theorem to the case of ∂ ¯ -closed smooth ( n − 1 , q ) -forms. Finally, we prove that the twist factor in the twisted Bochner–Kodaira identity can be a non-smooth plurisuperharmonic function.
Andrea Marchese - One of the best experts on this subject based on the ideXlab platform.
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kirszbraun s Extension Theorem fails for almgren s multiple valued functions
arXiv: Metric Geometry, 2014Co-Authors: Philippe Logaritsch, Andrea MarcheseAbstract:We show that there is no analog of Kirszbraun's Extension Theorem for Almgren's multiple valued functions.
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kirszbraun s Extension Theorem fails for almgren s multiple valued functions
Archiv der Mathematik, 2014Co-Authors: Philippe Logaritsch, Andrea MarcheseAbstract:We prove that in general it is not possible to extend a Lipschitz multiple valued function without increasing the Lipschitz constant, i.e. we show that there is no analog of Kirszbraun’s Extension Theorem for Almgren’s multiple valued functions.
