given an affine coxeter group w, the corresponding shi arrangement is a refinement of the corresponding coxeter hyperplane arrangements which was introduced by shi to study the kazhdan-lusztig cells for w. shi showed, in particular, that each region of a shi arrangement contains exactly one element in w of minimal length. garside shadows in w were introduced to study the word problem of the corresponding artin-tits (braid) group and turns out to produce automata to study the combinatorics of reduced words in w. in this talk, we will discuss the following conjecture: the set of minimal length elements of the regions in a shi arrangement is a garside shadow. the talk will be illustrated by the example of the affine symmetric group.