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C*-algebras and Elliptic Theory II pp 123–144Cite as

Adiabatic Limits and the Spectrum of the Laplacian on Foliated Manifolds

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Part of the book series: Trends in Mathematics ((TM))

Abstract

We present some recent results on the behavior of the spectrum of the differential form Laplacian on a Riemannian foliated manifold when the metric on the ambient manifold is blown up in directions normal to the leaves (in the adiabatic limit).

Supported by the Russian Foundation of Basic Research (grant no. 06-01-00208).

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Russian Academy of Sciences, 112 Chernyshevsky str., 450077, Ufa, Russia

    Yuri A. Kordyukov

  2. Department of Mathematics, Ufa State Aviation Technical University, 12 K. Marx str., 450000, Ufa, Russia

    Andrey A. Yakovlev

Authors
  1. Yuri A. Kordyukov
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  2. Andrey A. Yakovlev
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Ohio State University, 231 West 18th Avenue, Columbus, OH, 43210, USA

    Dan Burghelea

  2. Department of Mathematics, Massachusetts Institute of Technology, Room 2-174 77 Massachusetts Avenue, Cambridge, MA, 02139, USA

    Richard Melrose

  3. Department of Mechanics and Mathematics, Moscow State University, Leninskie Gory, 119992, Moscow, Russia

    Alexander S. Mishchenko  & Evgenij V. Troitsky  & 

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Kordyukov, Y.A., Yakovlev, A.A. (2008). Adiabatic Limits and the Spectrum of the Laplacian on Foliated Manifolds. In: Burghelea, D., Melrose, R., Mishchenko, A.S., Troitsky, E.V. (eds) C*-algebras and Elliptic Theory II. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8604-7_6

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