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A stationary harmonic map with a nonstationary tangent map
Abstract
We construct a stationary weakly harmonic map from a domain in \R^5 into a compact Kähler surface for which a tangent map is weakly harmonic but nonstationary. The target manifold is the blow-up of \CP^1\times\CP^1 at four points lying in one fiber and arranged at the vertices of a regular tetrahedron. The nonstationarity of the tangent map arises from the break down of the tetrahedral symmetry in the defect measure concentrated on the vertices.
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BibTeX
@misc{li2026stationary,
title = {{A stationary harmonic map with a nonstationary tangent map}},
author = {Siran Li and Zijun Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17938},
eprint = {2610.17938},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17938},
}
RIS
TY - UNPB
TI - A stationary harmonic map with a nonstationary tangent map
AU - Siran Li
AU - Zijun Wang
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.17938
UR - https://arxiv.org/abs/2610.17938
AB - We construct a stationary weakly harmonic map from a domain in \R^5 into a compact Kähler surface for which a tangent map is weakly harmonic but nonstationary. The target manifold is the blow-up of \CP^1\times\CP^1 at four points lying in one fiber and arranged at the vertices of a regular tetrahedron. The nonstationarity of the tangent map arises from the break down of the tetrahedral symmetry in the defect measure concentrated on the vertices.
ER -