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.
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.
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.