Exponential map and normal form for cornered asymptotically hyperbolic metrics

McKeown, Stephen

doi:10.1090/tran/7680

Author: 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
Published electronically: May 20, 2019
MathSciNet review: 4009432
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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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