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Adiabatic limits, vanishing theorems and the noncommutative residue

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Abstract

In this paper, we compute the adiabatic limit of the scalar curvature and prove several vanishing theorems by taking adiabatic limits. As an application, we give a Kastler-Kalau-Walze type theorem for foliations.

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Authors and Affiliations

  1. Center of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, China

    KeFeng Liu & Yong Wang

  2. Department of Mathematics, University of California at Los Angeles, Los Angeles, CA, 90095-1555, USA

    KeFeng Liu

  3. School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, China

    Yong Wang

Authors
  1. KeFeng Liu
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  2. Yong Wang
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Corresponding author

Correspondence to Yong Wang.

Additional information

Dedicated to Professor ZHONG TongDe on the occasion of his 80th birthday

This work was supported by National Natural Science Foundation of USA (Grant No. DMS0705284) and National Natural Science Foundation of China (Grant No. 10801027)

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Liu, K., Wang, Y. Adiabatic limits, vanishing theorems and the noncommutative residue. Sci. China Ser. A-Math. 52, 2699–2713 (2009). https://doi.org/10.1007/s11425-009-0214-4

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  • DOI: https://doi.org/10.1007/s11425-009-0214-4

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