Project 10: "Subdivision in nonlinear geometries, and discrete differential geometry"

This project is running since 2010.

Principal investigator: Johannes Wallner
Graz University of Technology, Austria.
Mentor for: Yang, Hammer; Ferizovic, Moßhammer; Boiko, Frei.

DK Students

  • Third phase of the doctoral program:
  • Felix Dellinger (Austria; since July 2020)
    Mentors: Thuswaldner, Müller.
  • Second phase of the doctoral program:
  • Svenja Hüning (Germany, April 2016–August 2019)
    Mentors: Michael Kerber, Birgit Vogtenhuber
    Thesis Title: "Convergence analysis of nonlinear refinement rules".
    PhD Defense: August 8, 2019.
    Referees: C. Conti (Florenz), T. Sauer (Passau), J. Wallner.
    Examiners: T. Sauer (Passau), J. Wallner.

  • First phase of the doctoral program:
  • Oliver Ebner (Austria; July 2010–July 2012)
    Personal homepage; Email:
    Mentors: Rainer Burkard, Wolfgang Woess.
    PhD Defense: July 20, 2012.
    Referees: Ph. Grohs (Zürich), K. Jetter (Stuttgart), J. Wallner.
    Examiners: Ph. Grohs (Zürich), J. Wallner.

Associated Students

  • Second phase of the doctoral program:
  • Leonardo Alese (Italy; November 2015–October 2020)
    Mentors: Peter Grabner, Daniele D'Angeli.
    Thesis Title: "Curved-crease surfaces".
    PhD Defense: October 30, 2020.
    Referees: T.Hoffmann (München), H. Pottmann (Wien), J. Wallner
    Examiners: H. Pottmann (Wien), J. Wallner.

  • Caroline Moosmüller (Austria; November 2013–February 2017)
    Mentors: Mihyun Kang, Roswitha Rissner.
    Thesis Title: "Smoothness analysis of linear and nonlinear Hermite subdivision schemes".
    PhD Defense: February 17, 2017.
    Referees: J. Wallner, T. Sauer (Passau), C. Conti (Florence)
    Examiners: J. Wallner, T. Sauer (Passau).
  • First phase of the doctoral program:
  • Wolfgang Carl (Austria; December 2012–June 2016)
    Personal homepage; Email:
    Mentors: Mihyun Kang, Franz Lehner.
    Thesis Title: "Semidiscrete surfaces".
    PhD Defense: June 3, 2016.
    Referees: J. Wallner, T. Hoffmann (München), W. Rossmann (Kobe).
    Examiners: J. Wallner, T. Hoffmann (München).

  • Florian Lehner (Austria; July 2011–July 2014)
    Personal homepage; Email:
    Mentors: Wilfried Imrich, Bettina Klinz, Wolfgang Woess.
    PhD Defense: July 4, 2014.
    Referees: W. Imrich (Leoben), S. Klavzar (Ljubljana), J. Wallner.
    Examiners: W. Imrich (Leoben), S. Klavzar (Ljubljana).

Project description

Subdivision means the refinement of discrete data arranged either over regular grids or over more general meshes. Nonlinear data, which have values in manifolds or more general metric spaces are not accessible by the well-established linear theory. A well-researched special case of such data given by the cone of positive definite symmetric matrices which arise in diffusion-tensor imaging and whose treatment is facilitated by a symmetric space structure and a natural metric with the Cartan-Hadamard property. Our work revolves around proving convergence of refinement processes and investiating continuity properties of limits. We strive to establish a body of results which covers large classes of subdivision processes, recognizes sensible properties imposed on admissible input data, and is valid for a large classes of geometries.

Showcases for possible PhD themes can be found here.