This is a temporary schedule of our course.
Week 1: Covering Theorems, Minkowski dimension, Hausdorff dimension.
Reference: [Hei01] Chapter 1. [BP17] Chapter 1.
Week 2: Self similarlity, Frostman's theory
Reference: [BP17] Chapter 2,3.
Week 3: Capacity, graph of contionus function
Reference: [BP17] Chapter 3, 5.
Week 4: Break.
Week 5: Lipshitz functions, Modulus
Reference: [Hei01] Chapter 6, 7.
Week 6: Loewner spaces, Poincare Inequality
Reference: [Hei01] Chapter 8, 9.
Week 7: Quasisymmetry and related fucntions
Reference: [Hei01] Chapter 10,11,12. Papers.
Week 8: Quasisymmetry and Conformal dimension
Reference: [Hei01] Chapter 14, 15.
Week 9: Gromov-Hausdorff convergence, Weak tangents.
Reference: [BBI01] Chapter 7,8. [DS97] Chapter 8,9.
Week 10: Hyperbolic spaces, Hyperbolic groups, the boundary of hyperbolic groups.
Reference: [KB02] Section 1, 2, 3.
Week 11: Properties of hyperbolic groups.
Reference: [KB02] Section 3, 4, 8.
Week 12: Cannon conjecture, Kapovich-Kleiner conjecture.
Reference: [KB02] Section 9, 12. Papers.
We will spend the rest of the semester on related interesting topics and the student's presentation.
课程:
Topics in Geometric Topology