2 problems

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Carlotto–Schulz conjecture on embeddings of the three-torus in the four-sphere
Let $S^1\times S^1\times S^1$ be the three-torus, and let the hypertorus denote the standard embedding of this product in the four-sphere $\mathbf{S}^{4}$ . Carlotto–Schulz conjectu…
Conjectureopenconstant-mean-curvature minimal-hypersurfaces sphere-embeddingsarXiv posted 2 days ago
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Huang–Ji–Yin Gap Conjecture for CR embeddings between spheres
Huang–Ji–Yin Gap Conjecture. All such embeddings are necessarily contained in proper complex plane sections of the target sphere.
Conjectureopencr-geometry rigidity sphere-embeddingsarXiv posted 2 days ago

Carlotto–Schulz conjecture on embeddings of the three-torus in the four-sphere