Sharp inequalities for determinants of Toeplitz operators and dbar-Laplacians on line bundles

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dc.creatorBerman, Robert J.
dc.date2009-05-26
dc.date.accessioned2026-07-07T13:18:17Z
dc.date.available2026-07-07T13:18:17Z
dc.descriptionWe prove sharp inequalities for determinants of Toeplitz operators and twisted Laplace operators on the two-sphere, generalizing the Moser-Trudinger-Onofri inequality. In particular a sharp version of conjectures of Gillet-Soule and Fang motivated by Arakelov geometry is obtained; applications to SU(2)-invariant determinantal random point processes on the two-sphere are also discussed. The inequalities are obtained as corollaries of a general theorem about the maximizers of a certain non-local functional defined on the space of all positively curved Hermitian metrics on an ample line bundle over a compact complex manifold. This functional is an adjoint version, introduced by Berndtsson, of Donaldson's L-functional and generalizes the Ding-Tian functional whose critical points are Kahler-Einstein metrics. In particular, new proofs of some results in Kahler geometry are also obtained, including a lower bound on Mabuchi's K-energy and the uniqueness result for Kahler-Einstein metrics on Fano manifolds of Bando-Mabuchi.
dc.description38 pages, no figures
dc.identifierhttps://arxiv.org/abs/0905.4263
dc.identifierhttp://arxiv.org/abs/0905.4263
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/231382
dc.subjectComplex Variables
dc.subjectDifferential Geometry
dc.titleSharp inequalities for determinants of Toeplitz operators and dbar-Laplacians on line bundles
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