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| A Note on Vanishing Theorems on Non-pseudoconvex Complex Manifolds |
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Citation： |
Jun YAO,Qingchun JI.A Note on Vanishing Theorems on Non-pseudoconvex Complex Manifolds[J].Chinese Annals of Mathematics B,2026,(1):145~156 |
| Page view： 207
Net amount： 108 |
Authors： |
Jun YAO; Qingchun JI |
Foundation： |
National Natural Science Foundation of China (Nos. 12431005, 12571086) |
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| Abstract： |
In this paper, the authors introduce a Morse-theoretic condition under which the Levi form is allowed to have negative eigenvalues outside the critical locus of a real-valued exhaustion function. Under this condition, they prove new vanishing theorems for Dolbeault cohomology groups with values in holomorphic vector bundles. The results generalize classical vanishing theorems on pseudoconvex domains to a broader class of non-pseudoconvex complex manifolds. |
Keywords： |
Levi form Vanishing theorems Dolbeault cohomology Non-pseudoconvex |
Classification： |
32F10, 32F32, 32W05 |
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