Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Bott-Chern harmonic forms on Stein manifolds
HTML articles powered by AMS MathViewer

by Riccardo Piovani and Adriano Tomassini PDF
Proc. Amer. Math. Soc. 147 (2019), 1551-1564 Request permission

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
  • J.-P. Demailly, Complex Analytic and Differential Geometry, Université de Grenoble, Saint-Martin d’Hères, 2012.
  • Harold Donnelly, $L_2$ cohomology of pseudoconvex domains with complete Kähler metric, Michigan Math. J. 41 (1994), no. 3, 433–442. MR 1297700, DOI 10.1307/mmj/1029005071
  • Harold Donnelly and Charles Fefferman, $L^{2}$-cohomology and index theorem for the Bergman metric, Ann. of Math. (2) 118 (1983), no. 3, 593–618. MR 727705, DOI 10.2307/2006983
  • M. Gromov, Kähler hyperbolicity and $L_2$-Hodge theory, J. Differential Geom. 33 (1991), no. 1, 263–292. MR 1085144
  • R. K. Hind and A. Tomassini, On $L_2$-cohomology of almost Hermitian manifolds, arXiv:1708.06316.
  • Daniel Huybrechts, Complex geometry, Universitext, Springer-Verlag, Berlin, 2005. An introduction. MR 2093043
  • James Morrow and Kunihiko Kodaira, Complex manifolds, AMS Chelsea Publishing, Providence, RI, 2006. Reprint of the 1971 edition with errata. MR 2214741, DOI 10.1090/chel/355
  • Takeo Ohsawa, On the infinite dimensionality of the middle $L^2$ cohomology of complex domains, Publ. Res. Inst. Math. Sci. 25 (1989), no. 3, 499–502. MR 1018512, DOI 10.2977/prims/1195173354
  • M. Schweitzer, Autour de la cohomologie de Bott-Chern, preprint, arXiv:0709.3528v1 [math.AG].
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
  • 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