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Singular solutions from simple Euclidean Jordan algebras
Abstract
For every finite-dimensional simple Euclidean Jordan algebra V of rank at least three, we realize the function tr(x3)/|x| on its traceless subspace V0 as a C1,1∖ C2 viscosity solution of a uniformly elliptic equation F(D2 u)=0 in ℝdimV0. This unifies and extends earlier constructions from Cartan isoparametric cubics, Hsiang minimal cubics, and traceless real symmetric matrices.
Related
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BibTeX
@misc{chu2026singular,
title = {{Singular solutions from simple Euclidean Jordan algebras}},
author = {BaoZhi Chu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04378},
eprint = {2611.04378},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04378},
}
RIS
TY - UNPB
TI - Singular solutions from simple Euclidean Jordan algebras
AU - BaoZhi Chu
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04378
UR - https://arxiv.org/abs/2611.04378
AB - For every finite-dimensional simple Euclidean Jordan algebra V of rank at least three, we realize the function tr(x^3)/|x| on its traceless subspace V_0 as a C^1,1∖ C^2 viscosity solution of a uniformly elliptic equation F(D^2 u)=0 in ℝ^dimV_0. This unifies and extends earlier constructions from Cartan isoparametric cubics, Hsiang minimal cubics, and traceless real symmetric matrices.
ER -