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Consider a nontrivial solution to a semilinear elliptic system of first orderwith smooth coefficients defined over an $n$-dimensional manifold. Assume theoperator has the strong unique continuation property. We show that the zero setof the solution is contained in a countable union of smooth $(n-2)$-dimensionalsubmanifolds. Hence it is countably $(n-2)$-rectifiable and its Hausdorffdimension is at most $n-2$. Moreover, it has locally finite $(n-2)$-dimensionalHausdorff measure. We show by example that every real number between 0 and$n-2$ actually occurs as the Hausdorff dimension (for a suitable choice ofoperator). We also derive results for scalar elliptic equations of secondorder.Comment: 16 pages, LaTeX2e, 2 figs, uses pstricks macro packag

Zero sets of solutions to semilinear elliptic systems of first order