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Families of Conformally Covariant Differential Operators, Q-Curvature and Holography
TLDR
In this paper, the Paneitz operator and paneitz curvature are used to represent the Laplacian and Q-curvature, respectively, in the context of Conformally Covariant Families.Abstract:
Spaces, Actions, Representations and Curvature.- Conformally Covariant Powers of the Laplacian, Q-curvature and Scattering Theory.- Paneitz Operator and Paneitz Curvature.- Intertwining Families.- Conformally Covariant Families.read more
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Symmetry Breaking for Representations of Rank One Orthogonal Groups
Toshiyuki Kobayashi,Birgit Speh +1 more
TL;DR: In this paper, a symmetry breaking operator for the spherical principal series representations is introduced. But symmetry breaking operators are not restricted to the principal series representation, but also to the symmetric symmetry breaking for the complementary series.
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Singular Solutions of Fractional Order Conformal Laplacians
TL;DR: In this article, the singular sets of solutions of a natural family of conformally covariant pseudodifferential elliptic operators of fractional order were investigated, with the goal of developing generalizations of some well-known properties of the singular Yamabe problem.
Book
A Spinorial Approach to Riemannian and Conformal Geometry
TL;DR: In this article, the spectral properties of the Dirac operator on compact spin manifolds are studied and a self-contained presentation of the basic algebraic, geometrical, analytical and topological ingredients is carried out.
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Explicit Formulas for GJMS-Operators and Q-Curvatures
TL;DR: In this paper, GJMS-operators are defined in terms of Poincare-Einstein metrics and renormalized volume coefficients and derived explicit formulas for conformally covariant third and fourth powers of the Laplacian.
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Juhl's formulae for GJMS operators and Q-curvatures
TL;DR: In this paper, direct proofs of Juhl's formulae for GJMS operators and Q-curvatures are given starting from the original construction of gJMS.