Bounding the dimension of exceptional sets for orthogonal projections
Abstract
It is well known that if A ⊆ R n A\subseteq \mathbb {R}^n is an analytic set of Hausdorff dimension a a , then dim H ( π V A ) = min { a , k } \dim _H(\pi _VA)=\min \{a,k\} for a.e. V ∈ G ( n , k ) V\in G(n,k) , where G ( n , k ) G(n,k) denotes the set of all k k -dimensional subspaces of R n \mathbb {R}^n and π V \pi _V is the orthogonal projection of A A onto V V . In this paper we study how large the exceptional set { V ∈ G ( n , k ) ∣ dim H
Fields of Study & Subjects
Advanced Numerical Analysis Techniques
Advanced Optimization Algorithms Research
Optimization and Variational Analysis
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 10
- Pages
- 4257–4266
- Publication date
- 17 June 2026
- Language
- EN