The Dirac Operator on Spaces with Conical Singularities and Positive Scalar Curvatures

DOI10.2307/1999686zbMath0559.58024OpenAlexW4250575104MaRDI QIDQ5185752

Arthur W. Chou

Publication date: 1985

Full work available at URL: https://doi.org/10.2307/1999686

zbMATH Keywords

Dirac operatorpositive scalar curvatureindex theoremconical singularities

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Exotic index theories on manifolds (58J22) Global Riemannian geometry, including pinching (53C20) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (25)

The index of Dirac operators on incomplete edge spaces ⋮ Zeta regularized determinants for conic manifolds ⋮ Global Strichartz estimates for the Dirac equation on symmetric spaces ⋮ \(L^p\)-cohomology, heat semigroup and stratified spaces ⋮ The index formula for families of Dirac type operators on pseudomanifolds ⋮ Families index for manifolds with boundary, superconnections, and cones. I: Families of manifolds with boundary and Dirac operators ⋮ \(L^ 2\)-index formulae for perturbed Dirac operators ⋮ On the spectrum of spherical Dirac-type operators ⋮ Asymptotic properties of the heat kernel on conic manifolds ⋮ Families index for manifolds with boundary, superconnections and cones. II: The Chern character ⋮ Exotic expansions and pathological properties of \(\zeta\)-functions on conic manifolds ⋮ The Dirac spectrum on manifolds with gradient conformal vector fields ⋮ Spectral convergence on degenerating surfaces ⋮ The Chern-Connes character for the Dirac operator on manifolds with boundary ⋮ Index Theory for Perturbed Dirac Operators on Manifolds with Conical Singularities ⋮ Resolvents of cone pseudodifferential operators, asymptotic expansions and applications ⋮ Zeta function and regularized determinant on a disc and on a cone ⋮ Elliptic operators and higher signatures. ⋮ \(K\)-homology classes of Dirac operators on smooth subsets of singular spaces ⋮ The resolvent expansion for second order regular singular operators ⋮ The structure of GUT breaking by orbifolding ⋮ Gaps in the differential forms spectrum on cyclic coverings ⋮ Eta and rho invariants on manifolds with edges ⋮ Low energy limit for the resolvent of some fibered boundary operators ⋮ The scalar curvature in conical manifolds: some results on existence and obstructions

Cites Work

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• Spectral geometry of singular Riemannian spaces
• Positive scalar curvature and the Dirac operator on complete Riemannian manifolds
• Spin and scalar curvature in the presence of a fundamental group. I
• The classification of simply connected manifolds of positive scalar curvature
• Clifford bundles, immersions of manifolds and the vector field problem
• Analytic torsion and R-torsion of Riemannian manifolds
• Clifford modules
• The index of elliptic operators. III
• On the heat equation and the index theorem
• A special Stoke's theorem for complete Riemannian manifolds
• On the diffraction of waves by conical singularities. II
• Der erste Eigenwert des Dirac‐Operators einer kompakten, Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung
• Spectral asymmetry and Riemannian geometry. III
• On the spectral geometry of spaces with cone-like singularities
• The Identity of Weak and Strong Extensions of Differential Operators

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