## Exponential map and normal form for cornered asymptotically hyperbolic metrics

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- by Stephen E. McKeown PDF
- Trans. Amer. Math. Soc.
**372**(2019), 4391-4424

## 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
- 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.
- © Copyright 2019 Stephen E. McKeown
- Journal: Trans. Amer. Math. Soc.
**372**(2019), 4391-4424 - MSC (2010): Primary 53B20, 53C22
- DOI: https://doi.org/10.1090/tran/7680
- MathSciNet review: 4009432