Rectifiability of the singular strata for harmonic maps to Euclidean buildings

Abstract

We define a natural notion of the singular strata for harmonic maps into $F$-connected complexes (which include locally finite Euclidean buildings), and prove the rectifiability of these strata. We additionally establish bounds on the Minkowski content for certain quantitative strata, following the rectifiable Reifenberg program of [NV17]. This builds on a result of the second author [D], which showed that the full singular set is $(n-2)$-rectifiable.