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Adiabatic Limit, Heat Kernel and Analytic Torsion

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Metric and Differential Geometry

Part of the book series: Progress in Mathematics ((PM,volume 297))

Abstract

We study the uniform behavior of the heat kernel under the adiabatic limit using microlocal analysis and apply it to derive a formula for the analytic torsion.

Mathematics Subject Classification (2000). 58Jxx, 35K08, 57Q10.

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Author information

Authors and Affiliations

  1. Math. Dept., UCSB, Santa Barbara, 93106, CA, USA

    Xianzhe Dai

  2. Math. Dept., MIT, Cambridge, 02139, MA, USA

    Richard B. Melrose

Authors
  1. Xianzhe Dai
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  2. Richard B. Melrose
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Corresponding author

Correspondence to Xianzhe Dai .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of California, South Hall 6511, Santa Barbara, 93106, New Jersey, USA

    Xianzhe Dai

  2. , Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, 08854, New Jersey, USA

    Xiaochun Rong

Additional information

Dedicated to Jeff Cheeger for his 65th birthday

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Dai, X., Melrose, R.B. (2012). Adiabatic Limit, Heat Kernel and Analytic Torsion. In: Dai, X., Rong, X. (eds) Metric and Differential Geometry. Progress in Mathematics, vol 297. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0257-4_9

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