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- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Yamada Kotaro
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Fri5-6(H119A)
- Group
- -
- Course number
- MTH.B502
- Credits
- 1
- Academic year
- 2016
- Offered quarter
- 2Q
- Syllabus updated
- 2016/12/14
- Lecture notes updated
- 2016/7/27
- Language used
- Japanese
- Access Index
-
Course description and aims
Introduction to Minimal Surface Theory: Students are introduced to the classical theory of minimal surfaces.
Through the first variation formula of the area functional, the Plateau and Bernstein problems, and the Weierstrass representation formula, the relationship between differential geometry and analysis, in particular complex analysis, is explained.
Student learning outcomes
Introduction to the classical theory of minimal surfaces: Students will learn
(1) ideas of variational principles through the first variation formula of the area functional,
(2) classical results in differential geometry, e.g. the Plateau problem and Bernstein's theorem, and
(3) the relationship between differential geometry and complex analysis through the Weierstrass representation formula.
This course is a continuation of MTH.B501 Advanced Topics in Geometry.
Keywords
The variational formula, minimal surface, the Weierstrass representation formula, Complex Analysis
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
Standard lecture. Homeworks will be assigned in each class.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | The first variation of the Area functional and minimal surfaces | Details will be provided during each class session |
| Class 2 | The classical Examples | Details will be provided during each class session |
| Class 3 | The isothermal coordinates | Details will be provided during each class session |
| Class 4 | The classical Plateau problem | Details will be provided during each class session |
| Class 5 | Bernstein's theorem | Details will be provided during each class session |
| Class 6 | The Weierstrass representation formula | Details will be provided during each class session |
| Class 7 | Non-trivial Examples | Details will be provided during each class session |
| Class 8 | Complete minimal surfaces of finite total curvature | Details will be provided during each class session |
Textbook(s)
None required
Reference books, course materials, etc.
R. Osserman, A survay of minimal surfaces, Dover Publications, 1982.
Assessment criteria and methods
Graded by homeworks
Related courses
- MTH.B211 ： Introduction to Geometry I
- MTH.B212 ： Introduction to Geometry II
- MTH.B501 ： Advanced topics in Geometry E
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) is requir
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.
