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Collapsing and Dirac-type operators

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Publication:1611629
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DOI10.1023/A:1016247531019zbMath1001.58020arXivmath/0005009MaRDI QIDQ1611629

John Lott

Publication date: 21 August 2002

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0005009


zbMATH Keywords

collapseDirac-type operatorlimit of the spectrum


Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Spectral theory; eigenvalue problems on manifolds (58C40)


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Manifolds with small Dirac eigenvalues are nilmanifolds ⋮ Dirac operators for matrix algebras converging to coadjoint orbits ⋮ Continuity of Dirac spectra ⋮ Riemannian flows and adiabatic limits ⋮ $p$-spectrum and collapsing of connected sums ⋮ Dirac operators on hypersurfaces as large mass limits ⋮ Index theorems on manifolds with straight ends ⋮ Dirac operators with \(W^{1,\infty}\)-potential on collapsing sequences losing one dimension in the limit ⋮ The Dirac operator under collapse to a smooth limit space ⋮ Eigenvalues of Dirac operators for hyperbolic degenerations



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