Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Bott-Chern harmonic forms on Stein manifolds


Authors: Riccardo Piovani and Adriano Tomassini
Journal: Proc. Amer. Math. Soc. 147 (2019), 1551-1564
MSC (2010): Primary 32Q15, 32Q28
DOI: https://doi.org/10.1090/proc/14334
Published electronically: December 19, 2018
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 32Q15, 32Q28

Retrieve articles in all journals with MSC (2010): 32Q15, 32Q28


Additional 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
Email: adriano.tomassini@unipr.it

DOI: https://doi.org/10.1090/proc/14334
Keywords: Bott-Chern harmonic form, Stein manifold, $d$-bounded
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
Article copyright: © Copyright 2018 American Mathematical Society