Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 2 min ago
PreprintarXiv licencearXiv

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

  • Matteo Carducci
  • Bozhidar Velichkov
Open at sourcePDFDOICite

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.

Related

  1. An Alt-Caffarelli problem for elastic graphs
    Marius Müller
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  2. On the Energy Minimizing Problem in Plasma Dynamics
    Maurice de Gosson
    arXivPreprintarXiv licenceFull textMathematical physicsHigh-energy & particle physicsarXiv
  3. Risk-minimizing GUE-implementations of truthful reporting in a Dynamic Social Choice Problem
    Endre Csóka, Máté Viczián
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsProbabilityarXiv
  4. The Arbitrary-Placement Problem in Entropy-Minimizing Selection, and a Residual-Entropy Formulation
    Alyssa H. Shin, Claire H. Shin
    arXivPreprintarXiv licenceFull textGeneral mathematicsarXiv
  5. Mixed-Integer Second-Order Cone Formulations for the Euclidean Bottleneck Steiner Tree Problem in ℝd
    Gabriel P. Braun, Marcia Fampa, Nelson Maculan +1
    arXivPreprintarXiv licenceFull textOptimisation & controlarXiv

Cite

BibTeXRIS
BibTeX
@misc{carducci2026minimizing,
  title = {{A minimizing cone from Cartan polynomials in the Alt-Caffarelli problem}},
  author = {Matteo Carducci and Bozhidar Velichkov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.35179},
  eprint = {2609.35179},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.35179},
}
RIS
TY  - UNPB
TI  - A minimizing cone from Cartan polynomials in the Alt-Caffarelli problem
AU  - Matteo Carducci
AU  - Bozhidar Velichkov
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.35179
UR  - https://arxiv.org/abs/2609.35179
AB  - 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.
ER  -