Compact embedded $\lambda$-torus in Euclidean spaces

TL;DR

This paper constructs compact embedded $\lambda$-hypersurfaces with torus topology in Euclidean spaces, expanding the understanding of such geometric structures.

Contribution

It introduces the first known construction of compact embedded $\lambda$-tori in Euclidean spaces with specific topological and geometric properties.

Findings

Existence of compact embedded $\lambda$-tori in Euclidean spaces.

New methods for constructing $\lambda$-hypersurfaces with torus topology.

Potential applications in geometric analysis and topology.

Abstract

In this paper, we construct compact embedded $\lambda$-hypersurfaces with the topology of torus which are called $\lambda$-torus in Euclidean spaces $\mathbb {R}^{n+1}$.