scholarly journals THE FIRST COEFFICIENTS OF THE ASYMPTOTIC EXPANSION OF THE BERGMAN KERNEL OF THESpincDIRAC OPERATOR

2006 ◽  
Vol 17 (06) ◽  
pp. 737-759 ◽  
Author(s):  
XIAONAN MA ◽  
GEORGE MARINESCU
Keyword(s):  
Asymptotic Expansion ◽  
Bergman Kernel ◽  
Dirac Operators ◽  
Line Bundles ◽  
Tensor Powers

We establish the existence of the asymptotic expansion of the Bergman kernel associated to the spincDirac operators acting on high tensor powers of line bundles with non-degenerate mixed curvature (negative and positive eigenvalues) by extending [15]. We compute the second coefficient b1in the asymptotic expansion using the method of [24].

scholarly journals A direct approach to Bergman kernel asymptotics for positive line bundles

2008 ◽  
Vol 46 (2) ◽  
pp. 197-217 ◽  
Author(s):  
Robert Berman ◽  
Bo Berndtsson ◽  
Johannes Sjöstrand
Keyword(s):  
Bergman Kernel ◽  
Direct Approach ◽  
Line Bundles ◽  
Bergman Kernel Asymptotics ◽  
Positive Line

scholarly journals Asymptotic Expansion of the Bergman Kernel via Perturbation of the Bargmann–Fock Model

2015 ◽  
Vol 26 (4) ◽  
pp. 2602-2638 ◽  
Author(s):  
Hamid Hezari ◽  
Casey Kelleher ◽  
Shoo Seto ◽  
Hang Xu
Keyword(s):  
Asymptotic Expansion ◽  
Bergman Kernel

scholarly journals On the growth of von Neumann dimension of harmonic spaces of semipositive line bundles over covering manifolds

2016 ◽  
Vol 27 (11) ◽  
pp. 1650093 ◽  
Author(s):  
Huan Wang
Keyword(s):  
Line Bundle ◽  
Main Tool ◽  
Line Bundles ◽  
Harmonic Space ◽  
Dolbeault Cohomology ◽  
Harmonic Forms ◽  
Von Neumann ◽  
Hermitian Manifolds ◽  
Von Neumann Dimension ◽  
Tensor Powers

We study the harmonic space of line bundle valued forms over a covering manifold with a discrete group action, and obtain an asymptotic estimate for the von Neumann dimension of the space of harmonic [Formula: see text]-forms with values in high tensor powers of a semipositive line bundle. In particular, we estimate the von Neumann dimension of the corresponding reduced [Formula: see text]-Dolbeault cohomology group. The main tool is a local estimate of the pointwise norm of harmonic forms with values in semipositive line bundles over Hermitian manifolds.

scholarly journals On the asymptotic expansion of Bergman kernel

2004 ◽  
Vol 339 (3) ◽  
pp. 193-198 ◽  
Author(s):  
Xianzhe Dai ◽  
Kefeng Liu ◽  
Xiaonan Ma
Keyword(s):  
Asymptotic Expansion ◽  
Bergman Kernel

HEAT KERNELS FOR PERTURBED DIRAC OPERATORS ON EVEN-DIMENSIONAL MANIFOLDS WITH BOUNDED GEOMETRY

2003 ◽  
Vol 14 (01) ◽  
pp. 69-104 ◽  
Author(s):  
JEFFREY FOX ◽  
PETER HASKELL
Keyword(s):  
Asymptotic Expansion ◽  
Dirac Operator ◽  
Differential Forms ◽  
Dirac Operators ◽  
Heat Kernels ◽  
Dimensional Manifold ◽  
Heat Operator ◽  
Bounded Geometry

This paper establishes conditions under which one can use integrals of locally defined differential forms to give an asymptotic expansion of the supertrace of the heat operator associated with a perturbed Dirac operator on a complete noncompact even-dimensional manifold with bounded geometry.

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