Dirac operators with \(W^{1,\infty}\)-potential on collapsing sequences losing one dimension in the limit

DOI10.1007/s00229-018-1003-6zbMath1398.53057arXiv1707.00608OpenAlexW2791825504MaRDI QIDQ1785557

Saskia Roos

Publication date: 1 October 2018

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.00608

zbMATH Keywords

spectrumbounded sectional curvatureorientable limit spacesymmetric \(W^{1, \infty }\)-potential

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Spin and Spin({}^c) geometry (53C27) Global Riemannian geometry, including pinching (53C20) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Potential theory on Riemannian manifolds and other spaces (31C12)

Related Items (2)

Compactness of Dirac-Einstein spin manifolds and horizontal deformations ⋮ The Dirac operator under collapse to a smooth limit space

Cites Work

• Collapsing of Riemannian manifolds and eigenvalues of Laplace operator
• Collapsing Riemannian manifolds to ones of lower dimensions
• A boundary of the set of the Riemannian manifolds with bounded curvatures and diameters
• Spineurs, opérateurs de Dirac et variations de métriques. (Spinors, Dirac operators and variations of the metrics)
• Generalized Killing spinors and conformal eigenvalue estimates for \(\text{Spin}^c\) manifolds
• Collapsing and Dirac-type operators
• Collapsing and the differential form Laplacian: the case of a smooth limit space.
• Continuity of Dirac spectra
• Einstein manifolds
• Nilpotent Structures and Invariant Metrics on Collapsed Manifolds
• Geometric Structures of Collapsing Riemannian Manifolds I
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