An invariant related to the existence of conformally compact Einstein fillings
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- by Matthew J. Gursky, Qing Han and Stephan Stolz PDF
- Trans. Amer. Math. Soc. 374 (2021), 4185-4205 Request permission
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 $X$.References
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Additional Information
- Matthew J. Gursky
- Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
- MR Author ID: 343766
- 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
- MR Author ID: 167655
- Email: Stephan.A.Stolz.1@nd.edu
- 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. - © Copyright 2021 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 374 (2021), 4185-4205
- MSC (2020): Primary 53Z05
- DOI: https://doi.org/10.1090/tran/8308
- MathSciNet review: 4251226