Bott-Chern harmonic forms on Stein manifolds
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- by Riccardo Piovani and Adriano Tomassini
- Proc. Amer. Math. Soc. 147 (2019), 1551-1564
- DOI: https://doi.org/10.1090/proc/14334
- Published electronically: December 19, 2018
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Abstract:
Let $M$ be an $n$-dimensional $d$-bounded Stein manifold $M$, i.e., a complex $n$-dimensional manifold $M$ admitting a smooth strictly plurisubharmonic exhaustion $\rho$ and endowed with the Kähler metric whose fundamental form is $\omega =i\partial \overline {\partial }\rho$, such that $i\overline {\partial }\rho$ has bounded $L^\infty$ norm. We prove a vanishing result for $W^{1,2}$ harmonic forms with respect to the Bott-Chern Laplacian on $M$.References
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Bibliographic Information
- Riccardo Piovani
- Affiliation: Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Unità di Matematica e Informatica, Università degli Studi di Parma, Parco Area delle Scienze 53/A, 43124, Parma, Italy
- Email: riccardo.piovani@studenti.unipr.it
- Adriano Tomassini
- Affiliation: Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Unità di Matematica e Informatica, Università degli Studi di Parma, Parco Area delle Scienze 53/A, 43124, Parma, Italy
- MR Author ID: 362161
- Email: adriano.tomassini@unipr.it
- Received by editor(s): May 14, 2018
- Received by editor(s) in revised form: July 10, 2018
- Published electronically: December 19, 2018
- Additional Notes: This work was partially supported by the Project PRIN “Varietà reali e complesse: geometria, topologia e analisi armonica” and by GNSAGA of INdAM
- Communicated by: Filippo Bracci
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 1551-1564
- MSC (2010): Primary 32Q15, 32Q28
- DOI: https://doi.org/10.1090/proc/14334
- MathSciNet review: 3910420