“…If a projection point z lies on N it is contained in a neighborhood V z Ă N which is locally embedded and has radius uniformly bounded from below. On the other hand, if the projection point z lies on the limit set of N , then since our analysis is local, we can consider a uniform bound from below for the injective radius of the ambient space in order to guarantee the existence of a minimal neighborhood V z , with radius uniformly bounded from below, contained in the limit set of N , see the proof of [4, Thm.1.5] and [3]. As in the proof of Theorem 1.1, by Lemma 2.1, at each projection point z P V z , for every µ ą 0, we can choose an embedding supporting surface S µ z at z satisfying (see [10,Lemm.1]) y R cutpS µ z q and H µ z pzq ą ´µ.…”