Quantization and the Hessian of Mabuchi energy

DOI10.1215/00127094-1813524zbMath1262.32024arXiv1009.4543OpenAlexW3099558011MaRDI QIDQ691567

Joel Fine

Publication date: 3 December 2012

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.4543

zbMATH Keywords

quantizationconstant scalar curvaturebalanced embedding

Mathematics Subject Classification ID

Kähler manifolds (32Q15) Geometric quantization (53D50)

Related Items (13)

Stability and integration over Bergman metrics ⋮ Quantization of the Laplacian operator on vector bundles. I ⋮ Quantisation of extremal Kähler metrics ⋮ Anticanonically balanced metrics on Fano manifolds ⋮ Quantization of symplectic fibrations and canonical metrics ⋮ Spectral aspects of the Berezin transform ⋮ Kähler-Einstein metrics ⋮ On the composition of Berezin-Toeplitz operators on symplectic manifolds ⋮ An explicit formula for the Berezin star product ⋮ On the coefficients of the asymptotic expansion of the kernel of Berezin-Toeplitz quantization ⋮ Relative Chow stability and extremal metrics ⋮ A note on the Bergman kernel ⋮ A note on Berezin-Toeplitz quantization of the Laplace operator

Cites Work

• On a set of polarized Kähler metrics on algebraic manifolds
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• Calabi flow and projective embeddings
• K-energy maps integrating Futaki invariants
• Some symplectic geometry on compact Kähler manifolds. I
• Canonical coordinates and Bergmann metrics
• Toeplitz quantization of Kähler manifolds and \(gl(N)\), \(N\to \infty\) limits
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• Scalar curvature and projective embeddings. I
• Geometric analysis of Chow Mumford stability.
• Holomorphic Morse inequalities and Bergman kernels
• Stability, energy functionals, and Kähler-Einstein metrics
• The Monge-Ampère operator and geodesics in the space of Kähler potentials
• Space of Kähler Metrics (V) – Kähler Quantization
• Berezin–Toeplitz quantization on Kähler manifolds
• On the Calabi flow
• Scalar curvature and projective embeddings, II
• Complex Monge-Ampere and Symplectic Manifolds
• Scalar curvature, moment maps, and the Deligne pairing
• On the lower order terms of the asymptotic expansion of Tian-Yau-Zelditch
• Geometric criterion for Gieseker-Mumford stability of polarized manifolds
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