Communications in Analysis and Geometry

Volume 22 (2014)

Number 2

Zero sets of eigenspinors for generic metrics

Pages: 177 – 218

DOI: http://dx.doi.org/10.4310/CAG.2014.v22.n2.a1

Author

Andreas Hermann (Institut für Mathematik, Universität Potsdam, Germany)

Abstract

Let $M$ be a closed connected spin manifold of dimension $2$ or $3$ with a fixed orientation and a fixed spin structure. We prove that for a generic Riemannian metric on $M$ the non-harmonic eigenspinors of the Dirac operator are nowhere zero. The proof is based on a transversality theorem and the unique continuation property of the Dirac operator.

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