A spinorial characterization of hyperspheres
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Publication:376613
DOI10.1007/s00526-012-0560-xzbMath1286.53057OpenAlexW2043574588WikidataQ125857148 ScholiaQ125857148MaRDI QIDQ376613
Oussama Hijazi, Sebastían Montiel
Publication date: 5 November 2013
Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00526-012-0560-x
Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Applications of global differential geometry to the sciences (53C80) Spin and Spin({}^c) geometry (53C27) Global submanifolds (53C40) Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) (57R15)
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Cites Work
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- Differential geometry in the large. Seminar lectures New York University 1946 and Stanford University 1956. With a preface by S. S. Chern
- Conformal lower bounds for the Dirac operator of embedded hypersurfaces
- An upper bound for the first eigenvalue of the Dirac operator on compact spin manifolds
- A characteristic property of spheres
- Compact constant mean curvature surfaces in Euclidean three-space
- The Dirac spectrum
- New examples of constant mean curvature immersions of (2k-1)-spheres into euclidean 2k-space
- Minimal immersions of surfaces by the first eigenfunctions and conformal area
- Counterexample to a conjecture of H. Hopf
- A conformal lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors
- Spineurs, opérateurs de Dirac et variations de métriques. (Spinors, Dirac operators and variations of the metrics)
- Extrinsic bounds on \(\lambda_1\) of \(\Delta\) on a compact manifold
- On the first eigenvalue of the Laplacian for compact submanifolds of Euclidean space
- Parallel spinors and parallel forms
- Extrinsic bounds for eigenvalues of the Dirac operator
- Upper bounds for the first eigenvalue of the Dirac operator on surfaces
- Extrinsic Killing spinors
- Quaternionic holomorphic geometry: Plücker formula, Dirac eigenvalue estimates and energy estimates of harmonic \(2\)-tori.
- Dirac operators on hypersurfaces of manifolds with negative scalar curvature
- Harmonic spinors
- Eigenvalue boundary problems for the Dirac operator
- Lower bounds for the eigenvalues of the Dirac operator
- On non-simply connected manifolds with non-trivial parallel spinors
- Constant mean curvature surfaces constructed by fusing Wente tori
- The Willmore conjecure for immersed tori with small curvature integral
- The Einstein-Dirac equation on Riemannian spin manifolds
- A spinorial approach to Riemannian and conformal geometry
- Real Killing spinors and holonomy
- Metrics with harmonic spinors
- One cannot hear the shape of a drum
- Équations différentielles caractéristiques de la sphère
- Unicity of constant mean curvature hypersurfaces in some riemannian manifolds
- Can One Hear the Shape of a Drum?
- Dirac operator on embedded hypersurfaces
- Eigenvalues of the Dirac operator on manifolds with boundary
- Conformal geometry of surfaces in \(S^4\) and quaternions