School Colloquium——The Bonnet problem: Is a surface characterized by its metric and curvatures?
报告人：Alexander Bobenko (Technical University of Berlin)
时间：2026-05-22 14:00-15:00
地点：智华楼四元厅
报告摘要：
A longstanding problem in differential geometry, known as the Bonnet problem, is whether a compact surface is uniquely determined by its metric and mean curvature function. It is known that this is the case for generic surfaces, and also for topological spheres. We explicitly construct a pair of immersed tori in three-dimensional Euclidean space that are related by a mean curvature preserving isometry. These tori are the first examples of compact Bonnet pairs. Moreover, we prove these isometric tori are real analytic. This resolves also a second longstanding open problem on whether real analyticity of the metric already determines a unique compact immersion. Discrete differential geometry is used to find crucial geometric properties of surfaces. This is a joint work with Tim Hoffmann and Andrew Sageman-Furnas.
报告人简介：
Alexander Bobenko is a professor of Mathematics at the Technical University of Berlin, Germany. He earned his PhD in mathematical physics in 1985 from Steklov Mathematical Institute, St. Petersburg. Following his studies, he received the Alexander von Humboldt Foundation Fellowship and spent two years as a postdoc in Bonn and Berlin. His fields of interest include geometry, mathematical physics and applications - in particular differential geometry, discrete differential geometry, integrable systems, Riemann surfaces, and geometry processing.
