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Asymptotically Hyperbolic Manifolds with Boundary Conjugate Points but no Interior Conjugate Points

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Abstract

We construct non-trapping asymptotically hyperbolic manifolds with boundary conjugate points but no interior conjugate points

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Notes

  1. Throughout this paper, Greek indices run from 1 to n and Latin indices run from 0 to n.

  2. We use \({{\,\mathrm{Sec}\,}}\) for sectional curvature, as opposed to \(\sec \) which will be used for the secant of a real number.

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Acknowledgements

Research of N.E. was partially supported by the National Science Foundation under Grants Nos. DMS-1800453 and DMS-1265958 of Gunther Uhlmann. It was also partially supported by the National Science Foundation under Grant No. DMS-1440140 while N.E. was in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Fall 2019 semester. The content of this paper appears as Chapter 2 of the 2020 University of Washington Ph.D. thesis of N.E. entitled Geodesic X-Ray Transform on Asymptotically Hyperbolic Manifolds.

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  1. Department of Mathematics, University of Washington, Box 354350, Seattle, WA, 98195-4350, USA

    Nikolas Eptaminitakis & C. Robin Graham

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  1. Nikolas Eptaminitakis
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  2. C. Robin Graham
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Correspondence to C. Robin Graham.

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Eptaminitakis, N., Graham, C.R. Asymptotically Hyperbolic Manifolds with Boundary Conjugate Points but no Interior Conjugate Points. J Geom Anal 31, 6819–6844 (2021). https://doi.org/10.1007/s12220-020-00451-w

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  • DOI: https://doi.org/10.1007/s12220-020-00451-w

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