The Journal of Geometric Analysis

, Volume 25, Issue 2, pp 761–782 | Cite as

Asymptotic Expansion of the Off-Diagonal Bergman Kernel on Compact Kähler Manifolds

  • Zhiqin Lu
  • Bernard ShiffmanEmail author


We compute the first four coefficients of the asymptotic off-diagonal expansion in Shiffman and Zelditch (J. Reine Angew. Math. 544:181–222, 2002) of the Bergman kernel for the N-th power of a positive line bundle on a compact Kähler manifold, and we show that the coefficient b 1 of the N −1/2 term vanishes when we use a K-frame. We also show that all the coefficients of the expansion are polynomials in the K-coordinates and the covariant derivatives of the curvature and are homogeneous with respect to the weight w in Lu (Am. J. Math. 122(2):235–273, 2000).


Asymptotic expansion Bergman kernel Kähler manifold Positive line bundle Szegő kernel 

Mathematics Subject Classification

32L10 58J37 53D50 32Q15 


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Copyright information

© Mathematica Josephina, Inc. 2013

Authors and Affiliations

  1. 1.Department of MathematicsUC IrvineIrvineUSA
  2. 2.Department of MathematicsJohns Hopkins UniversityBaltimoreUSA

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