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On the existence of a closed, embedded, rotational \(\lambda \)-hypersurface

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Abstract

In this paper we show the existence of a closed, embedded \(\lambda \)-hypersurfaces \(\Sigma \subset \mathbb {R}^{2n}\). The hypersurface \(\Sigma \) is diffeomorphic to \(\mathbb {S}^{n-1} \times \mathbb {S}^{n-1} \times \mathbb {S}^1\) and exhibits \(SO(n) \times SO(n)\) symmetry. Our approach uses a “shooting method” similar to the approach used by McGrath in constructing a generalized self-shrinking “torus” solution to mean curvature flow. The result generalizes the \(\lambda \) torus found by Cheng and Wei.

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Correspondence to John Ross.

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Ross, J. On the existence of a closed, embedded, rotational \(\lambda \)-hypersurface. J. Geom. 110, 26 (2019). https://doi.org/10.1007/s00022-019-0483-1

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  • DOI: https://doi.org/10.1007/s00022-019-0483-1

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