Large Steklov eigenvalues with a prescribed embedded boundary

For every smooth compact connected embedded boundary of positive dimension, the first positive Steklov eigenvalue of its smooth embedded fillings is unbounded, provided the ambient codimension is at least two and a filling exists. The boundary remains fixed pointwise, and the fillings carry their induced Euclidean metrics; volume and topology are unrestricted. We give a detailed proof using intrinsic large-eigenvalue constructions and relative smooth approximation of short embeddings. This follows the relative Nash--Kuiper mechanism announced by Girouard and Polymerakis, with the boundary and arbitrary-curve applications written out explicitly.