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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

   
 
 

 

Exponential map and normal form for cornered asymptotically hyperbolic metrics


Author: Stephen E. McKeown
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 53B20, 53C22
DOI: https://doi.org/10.1090/tran/7680
Published electronically: May 20, 2019
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Abstract: This paper considers asymptotically hyperbolic manifolds with a finite boundary intersecting the usual infinite boundary, cornered asymptotically hyperbolic manifolds, and proves a theorem of Cartan-Hadamard-type near infinity for the normal exponential map on the finite boundary. As a main application, a normal form for such manifolds at the corner is then constructed, analogous to the normal form for usual asymptotically hyperbolic manifolds and suited to studying geometry at the corner. The normal form is at the same time a submanifold normal form near the finite boundary and an asymptotically hyperbolic normal form near the infinite boundary.


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Additional Information

Stephen E. McKeown
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195
Address at time of publication: Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544
Email: smckeown@math.princeton.edu

DOI: https://doi.org/10.1090/tran/7680
Received by editor(s): September 30, 2016
Received by editor(s) in revised form: August 25, 2018
Published electronically: May 20, 2019
Additional Notes: This research was partially supported by the National Science Foundation under RTG Grant DMS-0838212 and Grant DMS-1161283.
Article copyright: © Copyright 2019 Stephen E. McKeown