Remark on the off-diagonal expansion of the Bergman kernel on compact Kähler manifolds

Abstract

In this short note, we compare our previous works on the off-diagonal expansion of the Bergman kernel and the recent preprint of Lu-Shiffman (arxiv.1301.2166). In particular, we note that the vanishing of the coefficient of p^{-1/2} is implicitly contained in Dai-Liu-Ma's work (J. Differential Geom. 72 (2006), no. 1, 1-41) and was explicitly stated in our book (Holomorphic Morse inequalities and Bergman kernels, Progress in Math., vol. 254, Birkhäuser, 2007).

4 pages

Cited by in corpus (6)

• On a property of Bergman kernels when the Kähler potential is analytic
• Off-diagonal asymptotic properties of Bergman kernels associated to analytic Kähler potentials
• Quantitative upper bounds for Bergman kernels associated to smooth Kähler potentials
• Asymptotic properties of Bergman kernels for potentials with Gevrey regularity
• Scaling asymptotics for Szegő kernels on Grauert tubes
• Asymptotic expansion of the off-diagonal Bergman kernel on compact Kähler manifolds