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A minimizing cone from Cartan polynomials in the Alt-Caffarelli problem
- Published
- Source
- OpenAlex
- Published in
- arXiv (Cornell University)
- DOI
- 10.48550/arxiv.2609.35179
- Original
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Abstract
In this paper we study a class of 1-homogeneous solutions of the one-phase problem coming from the Cartan isoparametric cubic polynomials, which exist only in dimensions $d=5,8,14,26$. Our main result shows that they are unstable in dimensions $d=5,8,14$, and minimizing in dimension $d=26$. This provides the first example of a singular minimizing cone in the Alt-Caffarelli problem that is neither axially symmetric nor of Lawson-type.
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