On the image size of singular maps. I

Abstract

For fixed integers n > m > r l + 1 > 0 n > m > {r_l} + 1 > 0 , we establish a sharp upper bound for the Hölder differentiability class of singular maps f : R n → R m f:{{\mathbf {R}}^n} \to {{\mathbf {R}}^m} of subrank r l {r_l} whose images have positive Lebesgue m m -measure.