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About |
| This book is based on a course on the Differential Geometry of curves and
surfaces at Technische Universität Berlin. Unlike the common approach
in existing textbooks on this topic, there is a strong focus on variational
problems, ranging from elastic curves to surface that minimize area or Willmore
functional. We focus on topics that are useful for applications in science and
Computer Graphics. Most often these applications are concerned with finding the
shape of a curve or a surface that minimizes some physically meaningful energy.
We do not introduce manifolds as such but our approach provides preparation and
motivation for a follow-up course on manifolds. Nevertheless, we are able to cover
topics like the Gauss-Bonnet theorem for compact surfaces. |
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Differential Geometry: From Elastic Curves to Willmore Surfaces Ulrich Pinkall and Oliver Gross Birkhäuser Compact Textbooks in Mathematics (2024) DOI: https://doi.org/10.1007/978-3-031-39838-4 [Manuscript] |
Acknowledgement |
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This work was funded by the Deutsche Forschungsgemeinschaft (DFG - German Research Foundation) - Project-ID 195170736 - TRR109 "Discretization in Geometry and Dynamics" and the Open Access Publication Fund of TU Berlin. Additional support was provided by SideFX software. We sincerely thank Javier Villegas, Geoff Goss, and William Irvine for allowing us to use their images. |