I.Contentsㄩ
Euler characteristic, isoperimetric inequality, Wirtinger and Sobolev inequalities, Poincar谷- Hopf index theorem, Cauchy＊s rigidity of convex polyhedra, Cohn Vossen- Minkowsky congruence of ovaloids, closed surfaces with constant Gaussian curvature. Hopf- Alexandrov theorems on closed surface of constant mean curvature. Singularities of surfaces with contant negative Gaussian curvature.
II.Course prerequisiteㄩ
advanced calculus, linear algebra, and some basic knowledge on surface theory.
III.Reference material ( textbook(s) )ㄩ
Heinz Hopf: Differential Geometry in the Large ㄜ TextbookSpringer- Verlag, Lecture Notes in Mathematics, ㄒ1000.
IV.Grading schemeㄩ
This is a reading/ discussion course. Each student should prepare the materials before class. The performance on class is crucial for the grades of students.