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01389nam a2200181Ia 4500 |
| 001 |
10.1016-j.jmaa.2022.126431 |
| 008 |
220718s2022 CNT 000 0 und d |
| 020 |
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|a 0022247X (ISSN)
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| 245 |
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|a A twisted complex Brunn-Minkowski theorem
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| 260 |
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|b Academic Press Inc.
|c 2022
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| 856 |
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|z View Fulltext in Publisher
|u https://doi.org/10.1016/j.jmaa.2022.126431
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|a In his Annals of Mathematics paper [2], Berndtsson proves an important result on the Nakano positivity of holomorphic infinite-rank vector bundles whose fibers are Hilbert spaces consisting of holomorphic L2-functions with respect to a family of weight functions {e−φ(t,⋅)}t∈U, varying in t∈U⊂Cm, over a pseudoconvex domain. Using a variant of Hörmander's theorem due to Donnelly and Fefferman, we show that Berndtsson's Nakano positivity result holds under different (in fact, more general) curvature assumptions. This is of particular interest when the manifold admits a negative non-constant plurisubharmonic function, as these curvature assumptions then allow for some curvature negativity. We describe this setting as a “twisted” setting. © 2022 Elsevier Inc.
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|a Bergman kernels
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|a Curvature negativity
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|a L2 estimates for dbar
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|a Nakano positivity theorem
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|a Ainasse, E.M.
|e author
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| 773 |
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|t Journal of Mathematical Analysis and Applications
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