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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.35179

Authors: Carducci, Matteo, Velichkov, Bozhidar

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7214776959

Cites:

Cited by: 1

Related to: 10