Dirac eigenvalue estimates on two-tori

DOI10.1016/j.geomphys.2003.12.004zbMath1075.53041OpenAlexW1991768612MaRDI QIDQ557253

Bernd Ammann

Publication date: 23 June 2005

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

Full work available at URL: https://doi.org/10.1016/j.geomphys.2003.12.004

zbMATH Keywords

SpectrumDirac operatorLaplace operatorSpin structuresConformal metricsTwo-dimensional torus

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Spin and Spin({}^c) geometry (53C27)

Related Items

An eigenvalue comparison theorem for the Dirac operator on surfaces ⋮ Manifolds with small Dirac eigenvalues are nilmanifolds ⋮ Systolic inequalities and Massey products in simply-connected manifolds ⋮ Dirac eigenvalue estimates on two-tori ⋮ Boundary case of equality in optimal Loewner-type inequalities

Cites Work

• Dirac eigenvalue estimates on two-tori
• Dirac eigenvalue estimates on surfaces
• A conformal lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors
• Compact six-dimensional Kähler spin manifolds of positive scalar curvature with the smallest possible first eigenvalue of the Dirac operator
• An estimation for the first eigenvalue of the Dirac operator on closed Kähler manifolds of positive scalar curvature
• Extrinsic bounds for eigenvalues of the Dirac operator
• Eigenvalue estimates for the Dirac operator on quaternionic Kähler manifolds
• The isoperimetric inequality on a surface
• Harmonic spinors
• Curvature functions for compact 2-manifolds
• Zur Abhängigkeit des Dirac-operators von der Spin-Struktur
• Der erste Eigenwert des Dirac‐Operators einer kompakten, Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung
• Mean curvature flow and geometric inequalities
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