Differential Geometry From Elastic Curves to Willmore Surfaces

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Synopsis

This open access book covers the main topics for a course on the differential geometry of curves and surfaces. Unlike the common approach in existing textbooks, there is a strong focus on variational problems, ranging from elastic curves to surfaces that minimize area, or the Willmore functional. Moreover, emphasis is given 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 physically meaningful energy. Manifolds are not introduced as such, but the presented approach provides preparation and motivation for a follow-up course on manifolds, and topics like the Gauss-Bonnet theorem for compact surfaces are covered.

Book details

Edition:
2024
Series:
Compact Textbooks in Mathematics
Author:
Ulrich Pinkall, Oliver Gross
ISBN:
9783031398384
Related ISBNs:
9783031398377
Publisher:
Springer International Publishing
Pages:
N/A
Reading age:
Not specified
Includes images:
Yes
Date of addition:
2024-03-16
Usage restrictions:
Copyright
Copyright date:
2024
Copyright by:
The Editor 
Adult content:
No
Language:
English
Categories:
Mathematics and Statistics, Nonfiction