Journal of Differential Geometry

An Eigenvalue Estimate for the $\bar \partial$-Laplacian

Bo Berndtsson

Full-text: Open access

Abstract

We study the $\bar\partial$-Laplacian on forms taking values in Lk, a high power of a semipositive line bundle over a compact complex manifold, and give an estimate of the number of eigenvalues smaller than λ. Examples show that the estimate gives the right order of magnitude in terms of the two spectral parameters k and λ.

Article information

Source
J. Differential Geom., Volume 60, Number 2 (2002), 295-313.

Dates
First available in Project Euclid: 20 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1090351103

Digital Object Identifier
doi:10.4310/jdg/1090351103

Mathematical Reviews number (MathSciNet)
MR1938114

Zentralblatt MATH identifier
1042.58015

Citation

Berndtsson, Bo. An Eigenvalue Estimate for the $\bar \partial$-Laplacian. J. Differential Geom. 60 (2002), no. 2, 295--313. doi:10.4310/jdg/1090351103. https://projecteuclid.org/euclid.jdg/1090351103


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