Mathematical Research Letters

Volume 8 (2001)

Number 2

Dirac Operator on Embedded Hypersurfaces

Pages: 195 – 208



Oussama Hijazi

Sebastián Montiel

Xiao Zhang


New extrinsic lower bounds are given for the classical Dirac operator on the boundary of a compact domain of a spin manifold. The main tool is to solve some boundary problems for the Dirac operator of the domain under boundary conditions of Atiyah-Patodi-Singer type. Spinorial techniques are used to give simple proofs of classical results for compact embedded hypersurfaces.

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