Analysis of the horizontal Laplacian for the Hopf fibration

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dc.creatorBauer, Robert O.
dc.date2002-09-11
dc.date.accessioned2026-07-07T04:50:46Z
dc.date.available2026-07-07T04:50:46Z
dc.descriptionWe study the horizontal Laplacian $Δ^H$ associated to the Hopf fibration $S^3\to S^2$ 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 $Δ^H$. We express the Green functions for associated Poisson semigroups and obtain bounds for their contraction properties and Sobolev inequalities for $Δ^H$. The bounds and inequalities improve as $|k|$ increases.
dc.description19 pages
dc.identifierhttps://arxiv.org/abs/math/0209127
dc.identifierhttp://arxiv.org/abs/math/0209127
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64912
dc.subjectAnalysis of PDEs
dc.subjectDifferential Geometry
dc.subject35K05; 35P10; 58J35
dc.titleAnalysis of the horizontal Laplacian for the Hopf fibration
dc.typetext

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