How discrete differential geometry and visualization helped to solve a classical problem in differential geometry

Appears in collection : 2026 - T1 - WS2 - Bridging visualization and understanding in Geometry and Topology

We consider a classical problem in differential geometry, known as the Bonnet problem, whether a surface is characterized by a metric and mean curvature function. We explicitly construct a pair of immersed tori that are related by a mean curvature preserving isometry. This resolves a longstanding open problem on whether the metric and mean curvature function determine a unique compact surface. Visualizations based on structure preserving discretizations of Discrete Differential Geometry were used to find crucial geometric properties of surfaces. This is a joint work with Tim Hoffmann and Andrew Sageman-Furnas.

Information about the video

Date of recording 20/02/2026
Date of publication 23/02/2026
Institution IHP
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students, Students
Director(s) Service audiovisuel de l'IHP
Format MP4
Venue IHP - Hermite Amphitheater

Citation data

DOI 10.57987/IHP.2026.T1.WS2.009
Cite this video Bobenko, Alexander (20/02/2026). How discrete differential geometry and visualization helped to solve a classical problem in differential geometry. IHP. Audiovisual resource. DOI: 10.57987/IHP.2026.T1.WS2.009
URL https://dx.doi.org/10.57987/IHP.2026.T1.WS2.009

Domain(s)

Geometric Topology

Bibliography

A.I. Bobenko, T. Hoffmann, A. Sageman-Furnas, Compact Bonnet Pairs: isothermic tori with the same curvatures, Publ. math. IHES (2025) https://doi.org/10.1007/s10240-025-00159-z