Dr. Günter Paul Peters

Arbeitsgruppe Geometrie
Institut für Mathematik
Technischen Universität Berlin
Sekr. MA 8-3 / Straße des 17. Juni 136 / 10623 Berlin

Email: peters@math.tu-berlin.de
Telefon: +49 30 314 25777, Fax: +49 30 314 79282
Raum: MA 881


Mathematische Visualisierung I (WS 09/10), Studierendenseminar Differentialgeometrie (WS 09/10), Selected Topics in Discrete Differential Geometry and Visualization, Beijing, 2009 , Studierendenseminar Differentialgeometrie (SS 09), Mathematik für Physikerinnen und Physiker II (SS 09), Studierendenseminar Differentialgeometrie (WS 08/09), Analysis II für Ingenieure (WS 08/09) (Folien), Seminar: H-Flächen in S3 (SS 08), Differentialgeometrie I: Kurven und Flächen (SS 08), Differentialgeometrie II: Mannigfaltigkeiten (WS 07/08), Seminar: Differentialgeometrie (WS 07/08), Analysis II für Ingenieure (WS 07/08), Differentialgeometrie I: Kurven und Flächen (SS 07), Differentialgeometrie II: Mannigfaltigkeiten (WS 06/07), Analysis I für Ingenieure (WS 06/07), Seminar: Differentialgeometrie (WS 06/07), Seminar: Diskrete Differentialgeometrie (SS 06), Einführungskurs Mathematik (SS 06), Einführungskurs Mathematik (WS 05/06), Differentialgeometrie II: Mannigfaltigkeiten (WS 05/06), Seminar: "Energien und Flüsse für Raumkurven" (WS 05/06), Seminar Diskrete Minimalflächen (SS 05), Mannigfaltigkeiten (WS 04/05), Seminar Willmore Flächen (WS 04/05), Analysis II für Ingenieure (WS 04/05), Analysis II für Ingenieure (SS 04), Analysis II für Ingenieure (WS 03/04), Analysis I für Ingenieure (SS 03), Seminar Differentialgeometrie (WS 02/03), Analysis III (WS 02/03), Analysis II (SS 02), Analysis I (WS 01/02), Analysis II für Ingenieure (SS 01), Analysis I für Ingenieure (WS 00/01), Höhere Mathematik III für Ingenieure (SS 00), Höhere Mathematik II für Ingenieure (WS 99/00), Höhere Mathematik I für Ingenieure (SS 99), Analysis I (WS 98/99).


  1. with Christoph Bohle:
    Soliton Spheres.
    to appear in Trans. Amer. Math. Soc., arXiv:0905.2162 [math.DG].

  2. with Christoph Bohle:
    Bryant surfaces with smooth ends.
    Comm. Anal. Geom., 17 (2009), no. 4, 587-619. (download pdf) arXiv: math/0411480 [math.DG]

  3. with Christoph Bohle and Ulrich Pinkall:
    Constrained Willmore surfaces.
    Calc. Var. Partial Differential Equations 32 (2008), 263-277. (online) arXiv: math/0411479 [math.DG]

  4. Darboux transformations: from elastic curves to elastic surfaces and beyond.
    In Franki Dillen, Ignace Van de Woestyne (Eds.) Pure and Applied Differential Geometry - PADGE 2007, Shaker, 2007. (online) (download pdf)

  5. Bryant surfaces with smooth ends.
    In Geometrie, (Oberwolfach, October 1-7, 2006). Organized by Victor Bangert, Yuri Burago and Ulrich Pinkall. Oberwolfach Rep. 3 (2006), no. 4, 2733-2736. (online) (download pdf)

  6. Soliton spheres,
    PhD thesis, Technische Universität Berlin, 2004, supervisor: Ulrich Pinkall. (online) (download pdf)

  7. Drehflächen und mKdV-Solitonen,
    Diplomarbeit, Technische Universität Berlin, 1998, Betreuung: Ulrich Pinkall. (download ps.gz) (download pdf)


Soliton Sphere Explorer

My main research subject at Technische Universität where the so called soliton spheres. This is a rich class of immersed spheres in the conformal 3- and 4-sphere that allows rational conformal parametrizations. For more details have a look at my publications.
Java Web Start of the Soliton Sphere Explorer

Explore Soliton Spheres.

Click on the screenshot to open the soliton sphere explorer as java web start application. Try the WASG keys to walk arround, the <Space> key to jump and the G-key to turn of gravitation, when you have jumped to some height. More...

To explore the different types of soliton spheres change the parameters in the panel with the title "Explore Soliton Spheres", which initially sits in the right hand slot.

The screenshot to the left shows a Willmore immersion of projective space, which has order 3. Have a look at a high resolution screenshot.

16π Willmore spheres

All Willmore spheres are soliton spheres. Here are some images of Willmore spheres with Willmore energy 16π:

blue yellow red purple

Movie "16π"


The movie "16π" explores the 2-parameter family of Willmore spheres connecting the Willmore sphere above. This movie was developed at SFB 288(Collaborative Research Centre) by Christoph Bohle, Uli Heller, Paul Peters, Klaus Thomas, (Music by Tim Hoffmann).

View the movie: 16pi.mp4 ([an error occurred while processing this directive]), 16pi_half.mpg ([an error occurred while processing this directive]),

Letzte Änderungen: 14.06.2010