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Bergman kernels and equilibrium measures for polarized pseudoconcave domains
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- Berman, Robert, 1976 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper, matematik,Department of Mathematical Sciences, Mathematics,University of Gothenburg,Chalmers tekniska högskola,Chalmers University of Technology
- (creator_code:org_t)
- 2010
- 2010
- English.
- In: International Journal of Mathematics. - 0129-167X. ; 21:1, s. 77-115
- Journal article (peer-reviewed)
Abstract
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- Let X be a domain in a closed polarized complex manifold (Y, L), where L is a (semi-) positive line bundle over Y. Any given Hermitian metric on L induces by restriction to X a Hilbert space structure on the space of global holomorphic sections on Y with values in the k-th tensor power of L (also using a volume form omega(n) on X). In this paper the leading large k asymptotics for the corresponding Bergman kernels and metrics are obtained in the case when X is a pseudo-concave domain with smooth boundary (under a certain compatibility assumption). The asymptotics are expressed in terms of the curvature of L and the boundary of X. The convergence of the Bergman metrics is obtained in a more general setting where (X, omega(n)) is replaced by any measure satisfying a Bernstein-Markov property. As an application the (generalized) equilibrium measure of the polarized pseudo-concave domain X is computed explicitly. Applications to the zero and mass distribution of random holomorphic sections and the eigenvalue distribution of Toeplitz operators will be described elsewhere.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
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- ref (subject category)
- art (subject category)
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