# On $\alpha$-minimizing hypercones

## TL;DR

This paper extends the class of known alpha-minimizing hypercones by analyzing special cubic and quartic polynomials using sub-calibration methods, advancing the understanding of minimal hypercone structures.

## Contribution

It introduces new alpha-minimizing hypercones through detailed polynomial analysis, significantly broadening the existing class of such hypercones.

## Key findings

- Expanded the class of known alpha-minimizing hypercones
- Developed new sub-calibration techniques for analysis
- Identified specific cubic and quartic polynomials related to hypercones

## Abstract

In this paper we considerably extend the class of known $\alpha$-minimizing hypercones using sub-calibration methods. Indeed, the improvement of previous results follows from a careful analysis of special cubic and quartic polynomials.