Under a linear spectral gap assumption on the Kodaira Laplacian, the paper proves asymptotic expansions and algebra properties for Toeplitz operators on non-compact manifolds, plus geometric conditions ensuring the gap on classes like Kähler-Einstein and quasi-projective manifolds.
FINSKI,Complex embeddings, Toeplitz operators and transitivity of optimal holomorphic extensions
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Algebraic obstructions control approximate WZW solutions on polarized families; a generalized equation using Harder-Narasimhan filtrations always has approximate solutions, and an asymptotic converse to the Andreotti-Grauert theorem is proved.
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Berezin-Toeplitz Quantization of non-compact manifolds
Under a linear spectral gap assumption on the Kodaira Laplacian, the paper proves asymptotic expansions and algebra properties for Toeplitz operators on non-compact manifolds, plus geometric conditions ensuring the gap on classes like Kähler-Einstein and quasi-projective manifolds.
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About Wess-Zumino-Witten equation and Harder-Narasimhan potentials
Algebraic obstructions control approximate WZW solutions on polarized families; a generalized equation using Harder-Narasimhan filtrations always has approximate solutions, and an asymptotic converse to the Andreotti-Grauert theorem is proved.