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Weak BLD mappings and Hausdorff measure (1703.06444v1)
Published 19 Mar 2017 in math.MG
Abstract: We prove that if $\Phi:X\to Y$ a mapping of weak bounded length distortion from a quasiconvex and complete metric space $X$ to any metric space $Y$, then for any Lipschitz mapping $f:\mathbb{R}k\supset E\to X$ we have that ${\mathcal H}k(f(E))=0$ in $X$ if and only if ${\mathcal H}k(\Phi(f(E)))=0$ in $Y$. This generalizes an earlier result of Haj\l{}asz and Malekzadeh where the target space $Y$ was a Euclidean space $Y=\mathbb{R}N$.