26,310 research outputs found
Jet isomorphism for conformal geometry
Jet isomorphism theorems for conformal geometry are discussed. A new proof of
the jet isomorphism theorem for odd-dimensional conformal geometry is outlined,
using an ambient realization of the conformal deformation complex. An infinite
order ambient lift for conformal densities in the case in which harmonic
extension is obstructed is described. A jet isomorphism theorem for even
dimensional conformal geometry is formulated using the inhomogeneous ambient
metrics recently introduced by the author and K. Hirachi.Comment: 29 pages, based on lectures delivered at the 2007 Winter School
'Geometry and Physics', Srni, Czech Republic; v.2 corrects typos introduced
by arXiv HyperTeX macr
Volume and Area Renormalizations for Conformally Compact Einstein Metrics
This article describes some geometric invariants and conformal anomalies for
conformally compact Einstein manifolds and their minimal submanifolds which
have recently been discovered via the Anti-de Sitter/Conformal Field Theory
correspondence.Comment: 15 pages, to appear Proc. of 19th Winter School in Geometry and
Physics, Srni, Czech Rep., Jan. 199
Conformal Powers of the Laplacian via Stereographic Projection
A new derivation is given of Branson's factorization formula for the
conformally invariant operator on the sphere whose principal part is the k-th
power of the scalar Laplacian. The derivation deduces Branson's formula from
knowledge of the corresponding conformally invariant operator on Euclidean
space (the k-th power of the Euclidean Laplacian) via conjugation by the
stereographic projection mapping.Comment: This is a contribution to the Proceedings of the 2007 Midwest
Geometry Conference in honor of Thomas P. Branson, published in SIGMA
(Symmetry, Integrability and Geometry: Methods and Applications) at
http://www.emis.de/journals/SIGMA
Search for star clusters close to the Galactic plane with DENIS
An automated search for star clusters close to the Galactic plane (|b| < 5
deg) was carried out on the Point Source Catalogue of the DENIS survey. 44% of
the Galactic plane have been observed and calibrated. The method allowed to
retrieve 22 known star clusters and to identify two new ones, not published yet
although previously presented in the 2MASS web site as embedded clusters in HII
regions. Extinction in the field and in front of the clusters are estimated
using a model of population synthesis. We present the method and give the
properties of these clusters.Comment: 5 pages, 3 figures, accepted for publication in A&
Scattering Matrix in Conformal Geometry
This paper describes the connection between scattering matrices on
conformally compact asymptotically Einstein manifolds and conformally invariant
objects on their boundaries at infinity. The conformally invariant powers of
the Laplacian arise as residues of the scattering matrix and Branson's
Q-curvature in even dimensions as a limiting value. The integrated Q-curvature
is shown to equal a multiple of the coefficient of the logarithmic term in the
renormalized volume expansion.Comment: 29 pages, 1 figur
Juhl's Formulae for GJMS Operators and Q-Curvatures
Direct proofs are given of Juhl's formulae for GJMS operators and
Q-curvatures starting from the original construction of GJMS.Comment: 18 page
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