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Analysis of the horizontal Laplacian for the Hopf fibration
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Robert O. Bauer
Published/Copyright:
November 18, 2005
Abstract
We study the horizontal Laplacian ΔH associated to the Hopf fibration S3 → S2 with arbitrary Chern number k. We use representation theory to calculate the spectrum, describe the heat kernel and obtain the complete heat trace asymptotics of ΔH. We express the Green functions for associated Poisson semigroups and obtain bounds for their contraction properties and Sobolev inequalities for ΔH. The bounds and inequalities improve as |k | increases.
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Published Online: 2005-11-18
Published in Print: 2005-11-18
Walter de Gruyter GmbH & Co. KG
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- Connections on principal bundles over Kähler manifolds with antiholomorphic involution
- Uniform distribution of the fractional part of the average prime divisor
- Analysis of the horizontal Laplacian for the Hopf fibration
- Algebraic inclusions of Moufang polygons
- Topological equivalence of linear representations for cyclic groups: II
- Capacities associated with Dirichlet space on an infinite extension of a local field
- The configuration space of arachnoid mechanisms
Articles in the same Issue
- Connections on principal bundles over Kähler manifolds with antiholomorphic involution
- Uniform distribution of the fractional part of the average prime divisor
- Analysis of the horizontal Laplacian for the Hopf fibration
- Algebraic inclusions of Moufang polygons
- Topological equivalence of linear representations for cyclic groups: II
- Capacities associated with Dirichlet space on an infinite extension of a local field
- The configuration space of arachnoid mechanisms
