Christian Miebach

ANR-DFG project QuaSiDy

Research Interests

• Geometric Invariant Theory on Kähler manifolds
• Geometry of actions of real-reductive Lie groups on real and complex manifolds admitting gradient maps
• Complex spherical varieties and spherical gradient manifolds
• Actions of discrete groups on hyperbolic Stein manifolds
• Bounded domains of holomorphy with non-compact automorphism group of positive dimension
• Stein and q-complete manifolds with many symmetries
• Globalizations of local holomorphic Lie group actions

Publications

• Matsuki's double coset decomposition via gradient maps,
  J. Lie Theory 18 (2008), no. 3, 555-580, download.
• Geometry of invariant domains in complex semi-simple Lie groups,
  Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 8 (2009), no. 3, 509-541, download.
• with Karl Oeljeklaus: On proper R-actions on hyperbolic Stein surfaces,
  Documenta Math. 14 (2009), 673-689, download.
• with Henrik Stötzel: Spherical gradient manifolds,
  Ann. Inst. Fourier (Grenoble) 60 (2010), no. 6, 2235-2260, download.
• Quotients of bounded homogeneous domains by cyclic groups,
  Osaka Journal of Mathematics 47 (2010), no. 2, 331-352, download.
• Sur les quotients discrets de semi-groupes complexes,
  Annales de la Faculté des Sciences de Toulouse (6) 19 (2010), no. 2, 269-276, download.
• with Bruce Gilligan and Karl Oeljeklaus: Homogeneous Kähler and Hamiltonian manifolds,
  Math. Ann. 349 (2011), no. 4, 889-901, download.
• with Daniel Greb: Invariant meromorphic functions on Stein spaces,
  Ann. Inst. Fourier (Grenoble) 62 (2012), no. 5, 1983-2011, download.
• with Bruce Gilligan and Karl Oeljeklaus: Pseudoconvex domains spread over complex homogeneous manifolds,
  Manuscripta Math. 142 (2013), no. 1-2, 35-59, download.
• Pseudoconvex non-Stein domains in primary Hopf surfaces,
  Izvestiya: Mathematics 78 (2014), no. 5, 1028-1035, download.
• with Lisa Knauss: Classification of spherical algebraic subalgebras of real simple Lie algebras of rank 1,
  J. Lie Theory 28 (2018), no. 1, 265-308, download.
• with Karl Oeljeklaus: Schottky group actions in complex geometry, in "Geometric Complex Analysis" (In Honor of Kang-Tae Kim’s 60th Birthday),
  Springer Proceedings in Mathematics & Statistics 246, Springer Nature, Singapore, 2018, 257-268, download.
• with Daniel Greb: Hamiltonian actions of unipotent groups on compact Kähler manifolds,
  Épijournal de Géométrie Algébrique 2 (2018), download.
• with Karl Oeljeklaus: Schottky groups acting on homogeneous rational manifolds,
  J. Reine Angew. Math. 753 (2019), 23-56, download.
• with Karl Oeljeklaus: Compact complex non-Kähler manifolds associated with totally real reciprocal units,
  Math. Z. 301 (2022), 2747-2760, download.
• with Daniel Greb: Momentum maps and the Kähler property for base spaces of reductive principal bundles,
  Proceedings of the Edinburgh Mathematical Society 66 (2023), no. 1, 218-230, download.
• On quotients of bounded homogeneous domains by unipotent discrete groups,
  to appear in the Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, download.

Preprints

Theses

• Geometry of invariant domains in complex semi-simple Lie groups,
  Dissertation, Ruhr-Universität Bochum, 2007, download.
• Discrete quotients of Stein manifolds, the geometry of holomorphic Lie group actions, and domains in complex homogeneous spaces,
  Thèse d'HDR, Université du Littoral Côte d'Opale, 2014, download.

Short CV