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Bergman kernels and equilibrium measures for polarized pseudoconcave domains

Robert Berman (Institutionen för matematiska vetenskaper, matematik)
International Journal of Mathematics (0129-167X). Vol. 21 (2010), 1, p. 77-115.
[Artikel, refereegranskad vetenskaplig]

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.


Denna post skapades 2010-02-19. Senast ändrad 2016-08-16.
CPL Pubid: 113205


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Institutionen för matematiska vetenskaper, matematik (2005-2016)



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