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Adiabatic Limit with Isolated Degenerate Fibres

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Microlocal Methods in Mathematical Physics and Global Analysis

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

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Abstract

In this talk I want to remind you of the setup for adiabatic limit and then to discuss various generalizations of it. I will try to show how problems with singular or degenerate fibres can be treated and how these are related to gluing problems and to the behaviour at the boundary of certain geometric moduli spaces.

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References

  1. Claudio Arezzo and Frank Pacard, On the Kähler classes of constant scalar curvature metrics on blow ups, arXiv:0706.1838.

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  2. Joel Fine, Constant scalar curvature kahler metrics on fibred complex surfaces, arXiv:0401275.

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  3. Chris Kottke and Richard Melrose, Generalized blow-up of corners and fiber products, Preprint April 2011.

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  4. E. Witten, Global gravitational anomalies, Commun. Math. Phys. 100 (1985), 197–229.

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Author information

Authors and Affiliations

  1. Department of Mathematics, MIT, Cambridge, MA, USA

    Richard B. Melrose

Authors
  1. Richard B. Melrose
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Correspondence to Richard B. Melrose .

Editor information

Editors and Affiliations

  1. Ammerländer Heerstr. 114-118, Oldenburg, 26111, Germany

    Daniel Grieser

  2. Inst. Mathematik, Universität Tübingen, Auf der Morgenstelle 10, Tübingen, 72076, Germany

    Stefan Teufel

  3. , Department of Mathematics, Bldg. 380, Stanford University, 450, Serra Mall, Stanford, 94305-2125, California, USA

    Andras Vasy

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Melrose, R.B. (2013). Adiabatic Limit with Isolated Degenerate Fibres. In: Grieser, D., Teufel, S., Vasy, A. (eds) Microlocal Methods in Mathematical Physics and Global Analysis. Trends in Mathematics(). Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0466-0_9

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