Rectifiability of the Singular Set of Harmonic Maps into Buildings
Ben Dees
TL;DR
This paper proves that the singular set of energy-minimizing harmonic maps into complex structures is rectifiable, enhancing previous regularity results and providing a geometric measure theory perspective.
Contribution
It establishes the rectifiability of the singular set for harmonic maps into buildings, extending Gromov and Schoen's regularity results.
Findings
Singular set is (m-2)-rectifiable.
Strengthens regularity results for harmonic maps.
Provides geometric measure theory insights.
Abstract
We prove that the singular set of an energy-minimizing map from Euclidean space into an -connected complex is -rectifiable. This strengthens the regularity result of Gromov and Schoen.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Markov Chains and Monte Carlo Methods