Mathematical Research Letters

Volume 8, Issue 2, March 2001 pp. 195-208.

Dirac Operator on Embedded Hypersurfaces

Authors: Oussama Hijazi, Sebastián Montiel and Xiao Zhang

Summary: 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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