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Transactions of the American Mathematical Society

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An invariant related to the existence of conformally compact Einstein fillings


Authors: Matthew J. Gursky, Qing Han and Stephan Stolz
Journal: Trans. Amer. Math. Soc.
MSC (2020): Primary 53Z05
DOI: https://doi.org/10.1090/tran/8308
Published electronically: March 2, 2021
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Abstract: We define an invariant for compact spin manifolds $ X$ of dimension $ 4k$ equipped with a metric $ h$ of positive Yamabe invariant on its boundary. The vanishing of this invariant is a necessary condition for the conformal class of $ h$ to be the conformal infinity of a conformally compact Einstein metric on $ X$.


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Additional Information

Matthew J. Gursky
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: mgursky@nd.edu

Qing Han
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: qhan@nd.edu

Stephan Stolz
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: Stephan.A.Stolz.1@nd.edu

DOI: https://doi.org/10.1090/tran/8308
Received by editor(s): January 25, 2019
Received by editor(s) in revised form: September 20, 2020
Published electronically: March 2, 2021
Additional Notes: The first author acknowledges the support of NSF grants DMS-1509633 and DMS-1547292.
The second author acknowledges the support of NSF grant DMS-1404596.
The third author acknowledges the support of NSF grant DMS-1547292.
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