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arXiv · 2609.35179

A minimizing cone from Cartan polynomials in the Alt-Caffarelli problem

Matteo Carducci·Bozhidar Velichkov
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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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Matteo Carducci, Bozhidar Velichkov. 2026-09-28. A minimizing cone from Cartan polynomials in the Alt-Caffarelli problem. https://arxiv.org/abs/2609.35179

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