This week we study how the Hausdorff dimension changes under orthogonal projection. We first begin by making sense of what we mean by ‘almost every plane’ by introducing the Grasmannian and its associated measure. Next, we introduce energies, a convenient object for estimating dimension that play well with projections.
- Notes: The Grasmannian, Dimensions of Projections
Alternatively: read Chapters 3, 8, and 9 of Mattila - Videos: The Grasmannian, Energies, Dimensions of Projections
- Exercises and Partial Solutions (prepare 1,2,4, and 5)