On the Existence of a Closed, Embedded, Rotational λ-Hypersurface
Ross, John
Original · EN
In this paper we show the existence of a closed, embedded λ-hypersurfaces Σ⊂ R²ⁿ. The hypersurface is diffeomorhic to Sⁿ⁻¹ × Sⁿ⁻¹ × S¹ and exhibits SO(n) × 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 λ-torus found by Cheng and Wei.
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