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EXPONENTIAL MAP AND NORMAL FORM FOR CORNERED ASYMPTOTICALLY HYPERBOLIC METRICS.
- Source :
- Transactions of the American Mathematical Society; 9/15/2019, Vol. 372 Issue 6, p4391-4424, 34p
- Publication Year :
- 2019
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- MANIFOLDS (Mathematics)
NORMAL forms (Mathematics)
INFINITY (Mathematics)
GEOMETRY
Subjects
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 372
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 138764301
- Full Text :
- https://doi.org/10.1090/tran/7680