Some progress in conformal geometry.
Chang, Sun-Yung A., Qing, Jie, Yang, Paul (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Chang, Sun-Yung A., Qing, Jie, Yang, Paul (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Olivier Biquard, Rafe Mazzeo (2006)
Archivum Mathematicum
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Gover, A.Rod (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Branson, Thomas P. (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Matthew Gursky, Jeffrey Streets, Micah Warren (2010)
Annales de l’institut Fourier
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Given a three-dimensional manifold with boundary, the Cartan-Hadamard theorem implies that there are obstructions to filling the interior of the manifold with a complete metric of negative curvature. In this paper, we show that any three-dimensional manifold with boundary can be filled conformally with a complete metric satisfying a pinching condition: given any small constant, the ratio of the largest sectional curvature to (the absolute value of) the scalar curvature is less than this...
Matthias Fischmann (2014)
Archivum Mathematicum
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The well known conformal covariance of the Dirac operator acting on spinor fields does not extend to its powers in general. For odd powers of the Dirac operator we derive an algorithmic construction in terms of associated tractor bundles computing correction terms in order to achieve conformal covariance. These operators turn out to be formally (anti-) self-adjoint. Working out this algorithm we recover explicit formula for the conformal third and present a conformal fifth power of the...