Concavity Property of Minimal $$L^{2}$$ Integrals with Lebesgue Measurable Gain VII–Negligible Weights

Bao, Shijie; Guan, Qi’an; Mi, Zhitong; Yuan, Zheng

doi:10.1007/978-981-99-9506-6_1

Springer Proceedings in Mathematics &Amp; Statistics

2024

DOI: 10.1007/978-981-99-9506-6_1

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Concavity Property of Minimal $$L^{2}$$ Integrals with Lebesgue Measurable Gain VII–Negligible Weights

Shijie Bao,

Qi’an Guan,

Zhitong Mi

et al.

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2024

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Cited by 3 publications

References 36 publications

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Boundary Points, Minimal L2 Integrals and Concavity Property III—Linearity on Riemann Surfaces and Fibrations over Open Riemann Surfaces

Guan,

Mi,

Yuan

2024

Acta. Math. Sin.-English Ser.

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Boundary Points, Minimal L2 Integrals and Concavity Property III—Linearity on Riemann Surfaces and Fibrations over Open Riemann Surfaces

Guan,

Mi,

Yuan

2024

Acta. Math. Sin.-English Ser.

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Optimal $$L^2$$ Extension for Holomorphic Vector Bundles with Singular Hermitian Metrics

Guan,

Mi,

Yuan

2024

Peking Math J

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Geometry of analytic continuation on complex manifolds – history, survey, and report

Ohsawa

2024

Complex Manifolds

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Beginning with the state of art around 1953, solutions of the Levi problem on complex manifolds will be recalled at first up to Takayama’s result in 1998. Then, the activity of extending the results by the L 2 {L}^{2} method in these decades will be reported. The method is by exploiting the finite dimensionality of certain L 2 {L}^{2} ∂ ¯ \bar{\partial } -cohomology groups to prove that a Hermitian holomorphic line bundle L L over a complex manifold M M is bimeromorphically equivalent to an ample bundle when it is restricted to a bounded locally pseudoconvex domain Ω ⋐ M \Omega \hspace{0.15em}\Subset \hspace{0.15em}M under the positivity of L ∣ ∂ Ω {L| }_{\partial \Omega } and the regularity of ∂ Ω \partial \Omega .

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Concavity Property of Minimal $$L^{2}$$ Integrals with Lebesgue Measurable Gain VII–Negligible Weights

Cited by 3 publications

References 36 publications

Boundary Points, Minimal L2 Integrals and Concavity Property III—Linearity on Riemann Surfaces and Fibrations over Open Riemann Surfaces

Boundary Points, Minimal L2 Integrals and Concavity Property III—Linearity on Riemann Surfaces and Fibrations over Open Riemann Surfaces

Optimal $$L^2$$ Extension for Holomorphic Vector Bundles with Singular Hermitian Metrics

Geometry of analytic continuation on complex manifolds – history, survey, and report

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