Existence of a constant-mean-curvature hypertorus in $S^4$ via computer assistance

Oscar Perdomo

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arXiv · 2506.19555

Existence of a constant-mean-curvature hypertorus in $S^4$ via computer assistance

Oscar Perdomo

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Abstract

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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Oscar Perdomo. 2025-06-24. Existence of a constant-mean-curvature hypertorus in $S^4$ via computer assistance. https://arxiv.org/abs/2506.19555

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