Construction of boundary invariants and the logarithmic singularity of the Bergman kernel
By K. Hirachi. 2000
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in which case the coefficients aj are expressed, by the Weyl invariant theory, in terms of the Riemannian curvature tensor and its covariant derivatives. The Bergman kernel’s counterpart of the time variable t is a defining function r of the domain Ω. By [F1] and [BS], the formal singularity of K at a boundary point p is uniquely determined by the Taylor expansion of r at p. Thus one has hope of expressing φ modulo On+1(r) and ψ modulo O∞(r) in terms of local biholomorphic invariants of the boundary, provided r is appropriately chosen. In [F3], Fefferman proposed to find such expressions by reducing the problem to an algebraic one in invariant theory associated with CR geometry, and indeed expressed φ modulo On−19(r) invariantly by solving the reduced problem partially. The solution in [F3] was then completed in [BEG] to give a full invariant expression of φ modulo On+1(r), but the reduction is still
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/8a15dc875c87971d38d400b1d26a1b167ab32ac8
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Tractor calculi for parabolic geometries (2001, background): “There has been considerable interest in the construction of polynomial invariants for parabolic structures [14, 15, 3, 24].”
- On the lower order terms of the asymptotic expansion of Tian-Yau-Zelditch (2000, background): “There are many studies of the Bergman and Szeg¨ o kernels on the pseudoconvex domain on n ([3], [4], [1], [6], [ 7 ] and [8], for example) following the”
- CR invariant powers of the sub-Laplacian (2003, background): “Kengo Hirachi has informed us that he has established the existence of such an operator in three dimensions mapping E(1, 1) → E(−3,−3) via the CR ambient metric with ambiguity derived in [26].”