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Existence of a constant-mean-curvature hypertorus in \(S^4\) via computer assistance

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arxiv 2506.19555 v1 pith:P3345YOP submitted 2025-06-24 math.DG

Oscar Perdomo This is my paper · ORCID
classification math.DG
keywords existencehypertorusmethodallowingapproximatingarithmeticassistancecomputer
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The round Taylor method uses rational arithmetic, allowing control of both round-off and truncation errors in approximating solutions of differential equations. In this paper, we employ this method together with the Poincare-Miranda theorem to prove the existence of a new embedded constant mean curvature (CMC) hypertorus in the unit four dimensional sphere

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  1. New Explicit Eigenfunctions of the stability operator on some minimal hypersurfaces

    math.DG 2026-07 accept novelty 5.0 of 10

    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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