## Conformal lower bounds for the Dirac operator of embedded hypersurfaces.(English)Zbl 1016.58013

Author’s abstract: We find sharp lower bounds for the first nonnegative eigenvalue of the classical intrinsic Dirac operator of a compact hypersurface bounding a domain in a Riemannian spin manifold. These estimates are given in terms of scalar (spectral) conformal invariants of the enclosed domain which are involved in the solution of the Yamabe problem.

### MSC:

 58J50 Spectral problems; spectral geometry; scattering theory on manifolds 53C20 Global Riemannian geometry, including pinching
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