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Boundary Problems for Dirac-Type Operators on Manifolds with Multi-Cylindrical End Boundaries

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Abstract

The goal of this paper is to establish a geometric program to study elliptic pseudodifferential boundary problems which arise naturally under cutting and pasting of geometric and spectral invariants of Dirac-type operators on manifolds with corners endowed with multi-cylindrical, or b-type, metrics and ‘b-admissible’ partitioning hypersurfaces. We show that the Cauchy data space of a Dirac operator on such a manifold is Lagrangian for the self-adjoint case, the corresponding Calderón projector is a b-pseudodifferential operator of order 0, characterize Fredholmness, prove relative index formulæ, and solve the Bojarski conjecture.

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Authors and Affiliations

  1. Department of Mathematics, Binghamton University, Vestal Parkway East, Binghamton, NY, 13902, U.S.A.

    Paul Loya

  2. School of Mathematics, Korea Institute for Advanced Study, 207-43, Cheongnyangni 2-dong, Dongdaemun-gu, Seoul, 130-722, Korea

    Jinsung Park

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  1. Paul Loya
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  2. Jinsung Park
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Correspondence to Paul Loya.

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Mathematics Subject Classifications (2000): 58J28, 58J52.

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Loya, P., Park, J. Boundary Problems for Dirac-Type Operators on Manifolds with Multi-Cylindrical End Boundaries. Ann Glob Anal Geom 29, 103–144 (2006). https://doi.org/10.1007/s10455-005-9004-6

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  • DOI: https://doi.org/10.1007/s10455-005-9004-6

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