Upper bounds for the first eigenvalue of the Dirac operator on surfaces

DOI10.1016/S0393-0440(98)00032-1zbMath0941.58018arXivmath/9806081WikidataQ115156418 ScholiaQ115156418MaRDI QIDQ1299204

Thomas Friedrich, Ilka Agricola

Publication date: 1 August 2000

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9806081

zbMATH Keywords

Dirac operatormean curvaturespin structurefirst eigenvaluesurfacesextrinsic upper bounds

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Global submanifolds (53C40) Global Riemannian geometry, including pinching (53C20) Surfaces in Euclidean and related spaces (53A05)

Related Items (8)

A spinorial characterization of hyperspheres ⋮ A sharp upper bound on the spectral gap for graphene quantum dots ⋮ Eigenvalue curves for generalized MIT bag models ⋮ Lower bounds for eigenvalues of the Dirac operator on \(n\)-spheres with \(SO(n)\)-symmetry ⋮ Eigenvalue estimates for Dirac operators with parallel characteristic torsion ⋮ A variational formulation for Dirac operators in bounded domains. Applications to spectral geometric inequalities ⋮ Lower bounds for eigenvalues of the Dirac operator on surfaces of rotation ⋮ Extrinsic eigenvalue estimates of Dirac operators on Riemannian manifolds

Cites Work

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• On the spinor representation of surfaces in Euclidean \(3\)-space
• Spectral estimates for Schrödinger and Dirac-type operators on Riemannian manifolds
• Zur Abhängigkeit des Dirac-operators von der Spin-Struktur

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