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- W3184757513 abstract "The first main result is a characterization of Nakano positivity of Riemannian vector bundles over bounded domains in terms of solvability of the d-equation with certain good L2 estimate condition. As an application, we give an alternative proof of the matrix-valued Prekopa's theorem that is originally proved by Raufi. The second main result contains a characterization of convexity of smoothly bounded domains in Rn in terms L2 estimate condition for the d-equation, and a characterization of pseudoconvexity of smoothly bounded domains in Cn in terms L2 estimate condition for the ∂¯-equation. Our methods are inspired by the recent works of Deng-Ning-Wang-Zhou on characterization of Nakano positivity of Hermitian holomorphic vector bundles and positivity of direct image sheaves associated to holomorphic fibrations." @default.
- W3184757513 created "2021-08-02" @default.
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- W3184757513 date "2021-11-01" @default.
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- W3184757513 title "Characterizations of curvature positivity of Riemannian vector bundles and convexity or pseudoconvexity of bounded domains in <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.svg><mml:msup><mml:mrow><mml:mi mathvariant=double-struck>R</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math> or <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si108.svg><mml:msup><mml:mrow><mml:mi mathvariant=double-struck>C</mml:mi></mml:mrow><mml…" @default.
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- W3184757513 doi "https://doi.org/10.1016/j.jfa.2021.109184" @default.
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