arXiv research

Formula for Bergman kernel of complex hyperbolic manifolds proved.

Study continuity of Bergman kernels on degenerating varieties.

Study Bergman kernels on Kähler manifolds, answering Lu-Tian's question.

Explicit formula for Bergman kernel of abelian varieties proved.

Paper compares Bergman kernel and Masur-Veech measure on Teichmüller space.

We study the asymptotic behavior of the generalized Bergman kernel of the renormalized Bochner-Laplacian on high tensor powers of a positive line bundle on a symplectic manifold of bounded geometry. First, we establish the off-diagonal exponential estimate for the generalized Bergman kernel. As an application, we obtai…

In this paper, we survey some recent results about the asymptotic expansion of Bergman kernel and we give a Bergman kernel proof of Kodaira embedding theorem.

Unified proofs of weak holomorphic Morse inequalities using Bergman kernel functions.

New method for spectral and Bergman kernels under local spectral gap condition.

Study Bergman kernel metrics on degenerating hyperelliptic surfaces.

Estimates Bergman kernel for positive line bundles.

Inspired by Berndtsson's work on the subharmonicity property of the Bergman kernel, we give a local variation formula of the full Bergman kernels associated to deformations of complex manifolds. In compact case, it follows from the reproducing property of the Bergman kernel and the curvature formula of the 0-th direct …

Study shows Bergman kernel quotient approaches one for punctured surfaces.

The paper studies invariant weighted Bergman metrics on domains.

We show that under very general assumptions the partial Bergman kernel function of sections vanishing along an analytic hypersurface has exponential decay in a neighborhood of the vanishing locus. Considering an ample line bundle, we obtain a uniform estimate of the Bergman kernel function associated to a singular metr…

The study shows algebraic Bergman kernels imply finite type boundaries in complex domains.

Using the techniques developed in \cite{SunSun}, we give estimations of the Bergman kernel of the punctured disk with the standard complete Poincaré metric. As an application, we improve the result of \cite{AMM} on the Bergman kernels of punctured Riemann surfaces near singularities.

Toeplitz operators linked to submultiplicative filtrations and weighted Bergman kernels.

Study shows Bergman kernels match averages on quotient spaces, proving non-vanishing of Poincaré series.

We prove an exponential estimate for the asymptotics of Bergman kernels of a positive line bundle under hypotheses of bounded geometry. We give further Bergman kernel proofs of complex geometry results, such as separation of points, existence of local coordinates and holomorphic convexity by sections of positive line b…

In this paper we consider a punctured Riemann surface endowed with a Hermitian metric which equals the Poincaré metric near the punctures and a holomorphic line bundle which polarizes the metric. We show that the Bergman kernel can be localized around the singularities and its local model is the Bergman kernel of the p…

Study Bergman kernels on complex hyperbolic cusps, generalizing previous results.

We establish the existence of the asymptotic expansion of the Bergman kernel associated to the spin-c Dirac operators acting on high tensor powers of line bundles with non-degenerate mixed curvature (negative and positive eigenvalues) by extending the paper " On the asymptotic expansion of Bergman kernel " (math.DG/040…

The Bergman kernel and period map for curves are studied.

We obtain several results about stability of the Bergman kernel on a tower of coverings on complex manifolds. An effective version of Rhodes' result is given for a tower of coverings on a compact Riemann surface of genus greater than or equal to 2. Stability of the Bergman kernel is established for towers of coverings …

The Bergman-Szegő kernel is analyzed for weakly pseudoconvex CR manifolds of finite type.

We give an alternate proof of the existence of the asymptotic expansion of the Bergman kernel associated to the $k$-th tensor powers of a positive line bundle $L$ in a $\frac{1}{\sqrt{k}}$-neighborhood of the diagonal using elementary methods. We use the observation that after rescaling the Kähler potential $k\varphi$ …

Study shows convergence of Bergman kernels on covering spaces of Kähler manifolds.

Study equivalence of metrics on noncompact Kähler manifolds with Bergman kernel properties.

We study the asymptotic of the Bergman kernel of the spin$^c$ Dirac operator on high tensor powers of a line bundle.

Master thesis proves Bergman kernel asymptotics for positive line bundles.

The paper discusses convergence of Bergman kernels on complex manifolds.

We establish an asymptotic expansion for families of Bergman kernels. The key idea is to use the superconnection as in the local family index theorem.

Study Bergman kernels and zero distributions of random sections on Kähler manifolds.

Study Bergman kernels on Kähler orbifolds with specific properties.

We provide a simple proof of a result of Rouby-Sjöstrand-Ngoc \cite{RSN} and Deleporte \cite{Deleporte}, which asserts that if the Kähler potential is real analytic then the Bergman kernel is an \textit{analytic kernel} meaning that its amplitude is an \textit{analytic symbol} and its phase is given by the polarization…

Study shows quantum behavior near infinity in metric asymptotics.

In this paper, we study the behavior of Bergman kernels along the Kähler Ricci flow on Fano manifolds. We show that the Bergman kernels are equivalent along the Kähler Ricci flow under certain condition on the Ricci curvature of the initial metric. Then, using a recent work of Tian and Zhang, we can solve a conjecture …

Two-dimensional domains with Kähler-Einstein Bergman metrics are biholomorphic to the unit ball.

The study examines Bergman kernels on complex manifolds with boundary and their asymptotic expansions.

We give a version of the comparison principle from pluripotential theory where the Monge-Ampère measure is replaced by the Bergman kernel and use it to derive a maximum principle

The study computes Bergman kernels and point process asymptotics on Kähler manifolds.

Study Bergman and spectral kernels for non-compact complex manifolds.

In this article, we derive off-diagonal estimates of the Bergman kernel associated to tensor- products of the cotangent line bundle defined over a hyperbolic Riemann surface of finite volume.

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…

Study asymptotics of extension and orthogonal Bergman kernels for high tensor powers of positive line bundles.

Study on zeros of Gaussian sections on semipositive line bundles on punctured Riemann surfaces.

We give a purely complex geometric proof of the existence of the Bergman kernel expansion. Our method provides a sharper estimate, and in the case that the metrics are real analytic, we prove that the remainder decays faster than any polynomial.