# Algebraic cmc hypersurface of order 3 in Euclidean spaces

## TL;DR

This paper proves that algebraic hypersurfaces of degree 3 in Euclidean spaces cannot have non-zero constant mean curvature, establishing a non-existence result for such geometric objects.

## Contribution

It provides a new non-existence theorem for algebraic hypersurfaces of degree 3 with constant mean curvature in Euclidean spaces.

## Key findings

- No algebraic hypersurfaces of degree 3 in ℝ^n have non-zero constant mean curvature.
- The result applies to all dimensions n.
- It advances understanding of the geometric properties of algebraic hypersurfaces.

## Abstract

We prove that there are not algebraic hypersurfaces of degree 3 in $\mathbb{R}^n$ with non zero constant mean curvature.