Year: 2026
Type: preprint
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}.
Source: arXiv (Cornell University)
Authors: Stoner, Ivy, Sun, Yitong
Institutions: Brown University, Johns Hopkins University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7206182519