New examples of higher-dimensional minimal hypersurfaces

TL;DR

This paper introduces a new method for constructing higher-dimensional minimal hypersurfaces in Euclidean space and demonstrates it with several novel examples, expanding the known catalog of such geometric objects.

Contribution

It provides an effective construction technique for minimal hypersurfaces and presents new explicit examples, advancing the understanding of higher-dimensional minimal geometry.

Findings

Effective construction method for minimal hypersurfaces

Several new explicit examples of higher-dimensional minimal hypersurfaces

Potential for further exploration of minimal hypersurface configurations

Abstract

The main results of the paper are Proposition 3 and 4 which provide an effective way to construct minimal hypersurfaces in a Euclidean space. We demonstrate our technique by several new examples. This note is English translation of an earlier draft version written (in Russian) in September 1999. The final version of the paper will be published somewhere else.