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2 results

  • TAME DISCRETE SUBSETS IN STEIN MANIFOLDS

  • Part of
  • JÖRG WINKELMANN
  • Journal:
    Journal of the Australian Mathematical Society / Volume 107 / Issue 1 / August 2019
    Published online by Cambridge University Press:
    26 December 2018, pp. 110-132
    Print publication:
    August 2019
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  • Rosay and Rudin introduced the notion of ‘tameness’ for discrete subsets of $\mathbf{C}^{n}$. We generalize the notion of tameness for discrete sets to arbitrary Stein manifolds, with special emphasis on complex Lie groups.

  • On Elliptic Curves in SL2(ℂ)/Γ.., Schanuel’s Conjecture and Geodesic Lengths

  • Jörg Winkelmann
  • Journal:
    Nagoya Mathematical Journal / Volume 176 / 2004
    Published online by Cambridge University Press:
    22 January 2016, pp. 159-180
    Print publication:
    2004
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  • Let Γ be a discrete cocompact subgroup of SL 2(ℂ). We conjecture that the quotient manifold X = SL 2(ℂ) / Γ contains infinitely many non-isogenous elliptic curves and prove this is indeed the case if Schanuel’s conjecture holds. We also prove it in the special case where Γ ∩ SL 2(∝) is cocompact in SL 2(ℝ).

    Furthermore, we deduce some consequences for the geodesic length spectra of real hyperbolic 2- and 3-folds.