Rectifiability of the Singular Strata for Harmonic Maps to DM-Complexes

Ivy Stoner; Yitong Sun

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arXiv · 2609.00183

Rectifiability of the Singular Strata for Harmonic Maps to DM-Complexes

Ivy Stoner·Yitong Sun

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Abstract

We prove a rectifiability theorem for harmonic maps into DM-complexes. More specifically, if $u$ is a harmonic map from a $n$-dimensional Riemannian domain to an $N$-dimensional NPC DM-complex $Y$, the $k$-th singular stratum of the singular set is countably $k$-rectifiable for all $k \in \{0,...,n-2\}.$ Our proof follows the framework in \cite{dm}. This extends the rectifiability result for the singular set of harmonic maps into a $F$-connected complex in \cite{dees} and generalizes the rectifiability theorem with respect the singular strata of harmonic maps into a $F$-connected complex in \cite{bd}.

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BibTeX RIS

Ivy Stoner, Yitong Sun. 2026-08-31. Rectifiability of the Singular Strata for Harmonic Maps to DM-Complexes. https://arxiv.org/abs/2609.00183

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