Chapter 1 Introduction ......................................... 1
Chapter 2 Coherent families of balls and planes ................ 9
Chapter 3 A partition of unity ................................ 13
Chapter 4 Definition of a mapping ƒ on Σ0 ..................... 15
Chapter 5 Local Lipschitz graph descriptions of the Σk ........ 19
Chapter 6 Reifenberg-flatness of the image .................... 27
Chapter 7 Distortion estimates for Dσk ........................ 31
Chapter 8 Holder and Lipschitz properties of ƒ on Σ0 .......... 37
Chapter 9 C2-regularity of the Σk and fields of linear
isometries defined on Σ0 ............................ 41
Chapter 10 The definition of g on the whole  n ................. 49
Chapter 11 Holder and Lipschitz properties of g on n .......... 55
Chapter 12 Variants of the Reifenberg theorem .................. 65
Chapter 13 Local lower-Ahlfors regularity and a better
sufficient bi-Lipschitz condition ................... 75
Chapter 14 Big pieces of bi-Lipschitz images and
approximation by bi-Lipschitz domains ............... 85
Chapter 15 Uniform rectifiability and Ahlfors-regular
Reifenberg-flat sets ................................ 91
Bibliography .................................................. 101
| 
