Bochner Laplacian and Bergman kernel expansion of semipositive line bundles on a Riemann surface

被引：2

作者：

Marinescu, George ^{[1
,2
]}

Savale, Nikhil ^{[1
]}

机构：

[1] Univ Cologne, Math Inst, Weyertal 86-90, D-50931 Cologne, Germany

[2] Romanian Acad, Inst Math Sim Stoilow, Bucharest, Romania

来源：

MATHEMATISCHE ANNALEN | 2024年 / 389卷 / 04期

关键词：

53C17; 58J50; 32A25; 53D50; DIFFERENTIAL-OPERATORS; ASYMPTOTICS; METRICS; ENERGY;

D O I：

10.1007/s00208-023-02750-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We generalize the results of Montgomery (Commun Math Phys 168:651-675, 1995) for the Bochner Laplacian on high tensor powers of a line bundle. When specialized to Riemann surfaces, this leads to the Bergman kernel expansion for semipositive line bundles whose curvature vanishes at finite order. The proof exploits the relation of the Bochner Laplacian on tensor powers with the sub-Riemannian (sR) Laplacian.

引用

页码：4083 / 4124

页数：42

共 39 条

[1] Agmon S, 1982, Mathematical Notes
[2] [Anonymous], 1996, Progress in Mathematics
[3] SCHRODINGER OPERATORS WITH MAGNETIC-FIELDS .1. GENERAL INTERACTIONS
AVRON, J
HERBST, I
SIMON, B
[J]. DUKE MATHEMATICAL JOURNAL, 1978, 45 (04) : 847 - 883
[4] BENAROUS G, 1989, ANN I FOURIER, V39, P73
[5] BERGMAN KERNELS AND EQUILIBRIUM MEASURES FOR LINE BUNDLES OVER PROJECTIVE MANIFOLDS
Berman, Robert J.
[J]. AMERICAN JOURNAL OF MATHEMATICS, 2009, 131 (05) : 1485 - 1524
[6] Berndtsson B, 2002, J DIFFER GEOM, V60, P295
[7] Bismut J.-M., 1992, I HAUTES ETUDES SCI, pii+298
[8] Bismut Jean-Michel, 1984, Progress in Mathematics, V45
[9] Catlin D, 1999, TRENDS MATH, P1
[10] ESTIMATES OF INVARIANT METRICS ON PSEUDOCONVEX DOMAINS OF DIMENSION-2
CATLIN, DW
[J]. MATHEMATISCHE ZEITSCHRIFT, 1989, 200 (03) : 429 - 466

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