Constructs embedded flat minimal tori in odd codimensions q≥3 with constant S+λ₂ values dense in (2,3), providing counterexamples to Lu's second-gap conjecture.
Minimal Hypersurfaces with constant scalar curvature in $\mathbf{S}^6$
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abstract
In this paper, we propose certain assumptions on the principal curvatures for a closed minimal hypersurface $M^5$ in $\mathbf{S}^6$ to be isoparametric, provided that the functions $S, f_3,f_4$ are constants. Our result removes the nonnegative scalar curvature assumption as in Tang and Yan \cite{TY}. Finally, as a rigidity result, if $M^5\subset \mathbf{S}^6$ has a point with exactly two distinct principal curvatures, then it must be a Clifford torus.
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math.DG 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Flat minimal tori and Lu's second-gap conjecture
Constructs embedded flat minimal tori in odd codimensions q≥3 with constant S+λ₂ values dense in (2,3), providing counterexamples to Lu's second-gap conjecture.