Modern tools in the theory of quasiconformal maps (Q2756937)

This concise text is a post graduate level course which introduces basic techniques in the geometric theory of quasiconformal maps in the Euclidean space \(\mathbb{R}^n\). The author has tried to develop these tools beyond \(\mathbb{R}^n\). The chief emphasis is the \(p\)-modulus of a family of path.NEWLINENEWLINENEWLINEThe contents are: 1. Modulus in a metric space. 2. Conformal modulus. 3. Definiton for quasiconformality. 4. Modulus estimates. 5. Upper gradients and \(\text{ACC}_p\) functions. 6. \(\text{ACC}_p\) functions in \(\mathbb{R}^n\). 7. Linear dilatation. 8. Analytic definition for quasiconformality. 9. \(\mathbb{R}^n\) as a Loewner space. 10. Quasisymmery.