Questions tagged [hausdorff-dimension]

Questions about dimensions of possibly highly irregular or "rough" sets, Hausdorff–Besicovitch dimension and related concepts such as box-counting or Minkowski–Bouligand dimension. To be used with [tag:fractals] or [tag:dimension-theory].

Filter by
Sorted by
Tagged with
3
votes
3answers
64 views

The Hausdorff dimension of the zero set of a real analytic function

Let $n>1$, and let $f:\mathbb{R}^n \to \mathbb{R}$ be a real-analytic function which is not identically zero. Does $\dim_{\mathcal H}(f^{-1}(0)) \le n-1$? here $\dim_{\mathcal H}$ refers to the ...