Bergman kernels on punctured Riemann surfaces

DOI10.1016/j.crma.2016.08.006zbMath1354.32002arXiv1604.06337OpenAlexW2963385051MaRDI QIDQ5890890

Xiaonan Ma, Hugues Auvray, George Marinescu

Publication date: 13 October 2016

Published in: Mathematische Annalen, Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.06337

zbMATH Keywords

Bergman kernelPoincaré metric, Kähler-Einstein metricpunctured Riemann Surfacespunctured Riemann surface

Mathematics Subject Classification ID

Determinants and determinant bundles, analytic torsion (58J52) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25) Riemann surfaces (30F99)

Related Items

Off-diagonal estimates of the Bergman kernel on hyperbolic Riemann surfaces of finite volume, Quotient of Bergman kernels on punctured Riemann surfaces, Approximation of regular Sasakian manifolds, Analytic torsion for surfaces with cusps. I: Compact perturbation theorem and anomaly formula, On the first order asymptotics of partial Bergman kernels, Analytic torsion for surfaces with cusps. II: Regularity, asymptotics and curvature theorem, Estimates of the Bergman kernel on a hyperbolic Riemann surface of finite volume. II, Bergman kernels on punctured Riemann surfaces, Bergman kernel on Riemann surfaces and Kähler metric on symmetric products, Projective embedding of log Riemann surfaces and K-stability, Bergman kernel asymptotics for singular metrics on punctured Riemann surfaces, Effective sup-norm bounds on average for cusp forms of even weight, Central charge from adiabatic transport of cusp singularities in the quantum Hall effect, Quantization and isotropic submanifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The space of Poincaré type Kähler metrics on the complement of a divisor
• Arithmetic characteristic classes of automorphic vector bundles
• On a set of polarized Kähler metrics on algebraic manifolds
• Complex immersions and Quillen metrics
• Hirzebruch's proportionality theorem in the non-compact case
• Points of small height on the modular curves \(X_0(N) \)
• Bounding the sup-norm of automorphic forms
• Convergence de la mêtrique de Fubini-Study d'un fibré linéaire positif. (Convergence of the Fubini-Study metric of a positive line bundle.)
• Comparison of Arakelov and Poincaré metrics on \(X_0(N)\)
• An arithmetic Riemann-Roch theorem
• Holomorphic Morse inequalities and Bergman kernels
• A remark on weighted Bergman kernels on orbifolds
• On the asymptotic behavior of Bergman kernels for positive line bundles
• Asymptotics of spectral function of lower energy forms and Bergman kernel of semi-positive and big line bundles
• Borcherds products and arithmetic intersection theory on Hilbert modular surfaces
• An arithmetic Hilbert–Samuel theorem for singular hermitian line bundles and cusp forms
• Berezin–Toeplitz quantization on Kähler manifolds
• Extremal metrics and K-stability
• Equidistribution results for singular metrics on line bundles
• Fibrés de higgs et connexions intégrables : Le cas logarithmique (diviseur lisse)
• On the first order asymptotics of partial Bergman kernels
• Orbifolds and analytic torsions
• Uniform Sup-Norm Bounds on Average for Cusp Forms of Higher Weights
• Asymptotic properties of extremal Kähler metrics of Poincaré type
• Bergman kernels on punctured Riemann surfaces
• Spectral theory of infinite-area hyperbolic surfaces
• On the asymptotic expansion of Bergman kernel