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New examples of constant mean curvature hypersurfaces in the sphere
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abstract
In this paper, firstly, we show the existence of a compact embedded constant mean curvature (CMC) hypersurface $\Sigma_1$ in $\mathbb{S}^{2n}$ of the type $S^{n-1} \times S^{n-1} \times S^{1}$. Moreover, the hypersurface $\Sigma_1$ exhibits $O(n)\times O(n)$ symmetry. Secondly, we show that there exists a compact embedded CMC-hypersurface $\Sigma_2 \subset \mathbb{S}^{3n-1}$ of the type $S^{n-1} \times S^{n-1} \times S^{n-1} \times S^{1}$. These results generalize the results of Carlotto and Schulz.
Forward citations
Cited by 3 Pith papers
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Existence of a constant-mean-curvature hypertorus in \(S^4\) via computer assistance
A rigorous computer-assisted proof establishes the existence of a new embedded constant mean curvature hypertorus in the four-dimensional unit sphere.
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Navigating the Space of Compact CMC Hypersurfaces in Spheres, Part II
A numerical one-parameter family of CMC hypersurfaces in S^4 connects a piecewise-CMC singular limit to a singular minimal limit, with a single non-embedded minimal member.
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New Explicit Eigenfunctions of the stability operator on some minimal hypersurfaces
For minimal immersions ϕ(y,z,t)=(f(t)y,f₂(t)z,f₁(t)), the functions ω(t)y_i z_j with ω=f^{-k}f₂^{-ℓ} are eigenfunctions of the stability operator for eigenvalue −n, implying index ≥ kℓ+3k+3ℓ+8.
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