Singularity Sets of Constant Principal Strain Deformations1

We show that if f is a mapping with constant principal strains (cps-mapping) of a planar domain of the form D\S, where D is itself a domain and S is a closed subset of D with linear measure 0, then f has an extension to a cps-mapping of D\S , where S ⊂ S has no accumulation points in D. The proof uses properties of cps-mappings attributable to the nonlinear hyperbolic nature of the underlying system of partial differential equations as well as results about their behavior in neighborhoods of isolated singularities previously established by the author.