Relevant bibliographies by topics / Tian-Yau-Zelditch expansion

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  2. Dissertations / Theses

Academic literature on the topic 'Tian-Yau-Zelditch expansion'

Author: Grafiati
Published: 9 March 2023

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Journal articles on the topic "Tian-Yau-Zelditch expansion"

1

LOI, ANDREA. "THE TIAN–YAU–ZELDITCH ASYMPTOTIC EXPANSION FOR REAL ANALYTIC KÄHLER METRICS." International Journal of Geometric Methods in Modern Physics 01, no. 03 (June 2004): 253–63. http://dx.doi.org/10.1142/s0219887804000162.

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Let M be a compact Kähler manifold endowed with a real analytic and polarized Kähler metric g and let Tmω(x) be the corresponding Kempf's distortion function. In this paper we compute the coefficients of Tian–Yau–Zelditch asymptotic expansion of Tmω(x) using quantization techniques alternative to Lu's computations in [10].
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2

Liu, Chiung-ju. "THE ASYMPTOTIC TIAN-YAU-ZELDITCH EXPANSION ON RIEMANN SURFACES WITH CONSTANT CURVATURE." Taiwanese Journal of Mathematics 14, no. 4 (August 2010): 1665–75. http://dx.doi.org/10.11650/twjm/1500405976.

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3

Arezzo, Claudio, and Andrea Loi. "Quantization of Kähler manifolds and the asymptotic expansion of Tian–Yau–Zelditch." Journal of Geometry and Physics 47, no. 1 (July 2003): 87–99. http://dx.doi.org/10.1016/s0393-0440(02)00175-4.

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4

Lu, Zhiqin. "On the lower order terms of the asymptotic expansion of Tian-Yau-Zelditch." American Journal of Mathematics 122, no. 2 (2000): 235–73. http://dx.doi.org/10.1353/ajm.2000.0013.

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5

Sena-Dias, Rosa. "Spectral measures on toric varieties and the asymptotic expansion of Tian-Yau-Zelditch." Journal of Symplectic Geometry 8, no. 2 (2010): 119–42. http://dx.doi.org/10.4310/jsg.2010.v8.n2.a1.

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6

LOI, ANDREA. "A LAPLACE INTEGRAL, THE T–Y–Z EXPANSION, AND BEREZIN'S TRANSFORM ON A KÄHLER MANIFOLD." International Journal of Geometric Methods in Modern Physics 02, no. 03 (June 2005): 359–71. http://dx.doi.org/10.1142/s0219887805000648.

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Let M be an n-dimensional complex manifold endowed with a C∞ Kähler metric g. We show that a certain Laplace-type integral ℒm(x), when x varies in a sufficiently small open set U ⊂ M, has an asymptotic expansion [Formula: see text], where Cr:C∞(U) → C∞(U) are smooth differential operators depending on the curvature of g and its covariant derivatives. As a consequence we furnish a different proof of Lu's theorem by computing the lower order terms of Tian–Yau–Zelditch expansion in terms of the operator Cj. Finally, we compute the differential operators Qj of the expansion Ber m(f) = Σr≥0m-rQr(f) of Berezin's transform in terms of the operators Cj.
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7

Liu, Chiung-Ju, and Zhiqin Lu. "Asymptotic Tian–Yau–Zelditch expansions on singular Riemann surfaces." Journal of Fixed Point Theory and Applications 10, no. 2 (September 21, 2011): 327–38. http://dx.doi.org/10.1007/s11784-011-0061-0.

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Dissertations / Theses on the topic "Tian-Yau-Zelditch expansion"

1

UCCHEDDU, DARIA. "The vanishing of the log term of the Szego kernel and Tian–Yau–Zelditch expansion." Doctoral thesis, Università degli Studi di Cagliari, 2015. http://hdl.handle.net/11584/266591.

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This thesis consists in two results. In [Z. Lu, G. Tian, The log term of Szego kernel, Duke Math. J. 125, N 2 (2004), 351-387], the authors conjectured that given a Kähler form ω on CPn in the same cohomology class of the Fubini–Study form ωFS and considering the hyperplane bundle (L; h) with Ric(h) = ω, if the log–term of the Szego kernel of the unit disk bundle Dh L vanishes, then there is an automorphism φ : CPn → CPn such that φω = ωFS. The first result of this thesis consists in showing a particular family of rotation invariant forms on CP2 that confirms this conjecture. In the second part of this thesis we find explicitly the Szego kernel of the Cartan–Hartogs domain and we show that this non–compact manifold has vanishing log–term. This result confirms the conjecture of Z. Lu for which if the coefficients aj of the TYZ expansion of the Kempf distortion function of a n– dimensional non–compact manifold M vanish for j > n, then the log–term of the disk bundle associated to M is zero.
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2

CAMOSSO, SIMONE. "Scaling asymptotics of Szego kernels under commuting Hamiltonian actions." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2015. http://hdl.handle.net/10281/77488.

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Let M be a connected d-dimensional complex projective manifold, and let A be a holomorphic positive Hermitian line bundle on M, with normalized curvature. Let G be a compact and connected Lie group of dimension d(G), and let T be a compact torus T of dimension d(T). Suppose that both G and T act on M in a holomorphic and Hamiltonian manner, that the actions commute, and linearize to A. If X is the principal circle-bundle associated to A, then this set-up determines commuting unitary representations of G and T on the Hardy space H(X) of X, which may then be decomposed over the irreducible representations of the two groups. If the moment map for the T-action is nowhere zero, all isotypical components for the torus are finite-dimensional, and thus provide a collection of finite-dimensional G-modules. Given a non-zero integral weight n(T) for T, we consider the isotypical components associated to the multiples kn(T), k that goes to infinity, and focus on how their structure as G-modules is reflected by certain local scaling asymptotics on X (and M). More precisely, given a fixed irreducible character n(G) of G, we study the local scaling asymptotics of the equivariant Szegő projectors associated to n(G) and kn(T), for k that goes to infinity, investigating their asymptotic concentration along certain loci defined by the moment maps.
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