Bulletin of the Korean Mathematical Society (대한수학회보)

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THE CONVEX HULL OF THREE BOUNDARY POINTS IN COMPLEX HYPERBOLIC SPACE

  • Kim, Youngju (Department of Mathematics Konkuk University)
  • Received : 2020.06.03
  • Accepted : 2020.08.21
  • Published : 2021.05.31
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Abstract

The convex hull of a generic triple of boundary points has non-zero finite volume in complex hyperbolic 2-space.

Keywords

Acknowledgement

The author would like to thank Bill Goldman for bringing this problem to our attention and the University Pierre et Marie Curie in Paris for their hospitality.

References

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  2. W. M. Goldman, Complex hyperbolic geometry, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1999.
  3. C. Hummel, U. Lang, and V. Schroeder, Convex hulls in singular spaces of negative curvature, Ann. Global Anal. Geom. 18 (2000), no. 2, 191-204. https://doi.org/10.1023/A:1006698910715
  4. J. R. Parker, Notes on complex hyperbolic geometry, Lecture Notes, 2010.
  5. C. Ramos-Cuevas, Convexity is a local property in CAT(κ) spaces, in Mexican mathematicians abroad: recent contributions, 189-196, Contemp. Math., 657, Aportaciones Mat, Amer. Math. Soc., Providence, RI. https://doi.org/10.1090/conm/657/13097