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- Academic unit or major
- Mathematics
- Instructor(s)
- Yamada Kotaro
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Tue3-4(H104)
- Group
- -
- Course number
- ZUA.B331
- Credits
- 1
- Academic year
- 2018
- Offered quarter
- 1Q
- Syllabus updated
- 2018/3/20
- Lecture notes updated
- 2018/4/9
- Language used
- Japanese
- Access Index
-
Course description and aims
As a special topic of the theory of surfaces in Euclidean space, introductory topics for surfaces of constant mean curvature are explained.
Student learning outcomes
Students are expected to learn
- that a surface of constant mean curvature is a stationary point of the area functional under the volume constraint,
- an elementary method to construct examples of constant mean curvature,
- and an outline of the proof of Alexandrov's theorem for closed surfaces of constant mean curvature.
Keywords
Surfaces of constant mean curvature, area functional, Alexandrov's theorem
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
A standard lecture course.
Homeworks will be assined for each lesson.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | The first variation formula of the area functional for surfaces. | Details will be provided during each class session |
| Class 2 | Characterization of surfaces of constant mean curvature | Details will be provided during each class session |
| Class 3 | Examples of surfaces of constant mean curvature | Details will be provided during each class session |
| Class 4 | Construction of constant mean curvature surfaces of revolution | Details will be provided during each class session |
| Class 5 | The differential equation for constant mean curvature graph | Details will be provided during each class session |
| Class 6 | Alexandrov's theorem | Details will be provided during each class session |
| Class 7 | Stability | Details will be provided during each class session |
Textbook(s)
No textbook is set.
Lecture note will be provided.
Reference books, course materials, etc.
Masaaki Umehara and Kotaro Yamada, Differential Geometry of Curves and Surfaces, Transl. by Wayne Rossman, World Scientific Publ., 2017, ISBN 978-9814740234 (hardcover); 978-9814740241 (softcover)
Katsuei Kenmotsu, Surfaces with constant mean curvature, Transl. by Katsuhiro Moriya, Translations of Mathematical Monographs, American Mathematical Society, 2003, ISBN 978-0821834794
Assessment criteria and methods
Graded by homeworks
Related courses
- MTH.B211 ： Introduction to Geometry I
- MTH.B212 ： Introduction to Geometry II
- MTH.B301 ： Geometry I
- MTH.B302 ： Geometry II
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Knowledge on differential geometry of curves and surfaces (as in MTH.B211 "Introduction to Geometry I" and MTH.B212 "Introduction to Geometry II", or Sections 1 to 10 of the text book "Differential Geometry of Curves and Surfaces" by M. Umehara and K.
Yamada), and knowledge of fundamental notions of differentiable manifolds (MTH.301/MTH.302) are required.
Contact information (e-mail and phone) Notice : Please replace from "[at]" to "@"(half-width character).
kotaro[at]math.titech.ac.jp
Office hours
N/A. Contact by E-mails, or at the classroom.
Other
For details, visit the web-site of this class http://www.math.titech.ac.jp/~kotaro/class/2018/geom-a
