A rigorous computer-assisted proof establishes the existence of a new embedded constant mean curvature hypertorus in the four-dimensional unit sphere.
Navigating the Space of Compact CMC Hypersurfaces in Spheres, Part I
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abstract
In this paper, we describe a family of embedded hypersurfaces with constant mean curvature (CMC) in the $(n+1)$-dimensional unit sphere. In the process, we provide evidence for new CMC embedded examples. In particular, for some examples with $H=0$, we verify Yau's conjecture stating that among the embedded, non-totally umbilical minimal hypersurfaces in spheres, the Clifford hypersurfaces have the least area.
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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.