Author

Cheng-Song You

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Preprint Sep 2026

Exchange complexes and contractibility of the complex of incompressible Seifert surfaces

Let $K\subset S^3$ be a non-trivial knot and let $\mathrm{IS}(K)$ be the simplicial complex whose vertices are the ambient isotopy classes of incompressible Seifert surfaces in the exterior $E(K)$, a finite set of distinct vertices spanning a simplex exactly when its classes admit simultaneously pairwise disjoint repre...

Guan-Cheng Pan, Cheng-Song You, Jun-Wei Zhou et al. · 0 citations

Preprint Sep 2026

Mockenhaupt's Three-Term Hardy-Littlewood Majorant Conjecture

For an integer $k \ge 0$, let $f_k(x) = 1 + e(x) + e((k+2)x)$ and $g_k(x) = 1 + e(x) - e((k+2)x)$ on $\mathbb{T} = \mathbb{R}/\mathbb{Z}$, where $e(x) = e^{2\pi i x}$. Mockenhaupt conjectured that $\|g_k\|_{L^p(\mathbb{T})}>\|f_k\|_{L^p(\mathbb{T})}$ whenever $2k<p<2k+2$. The conjecture was previously known for $k \le...

Guan-Cheng Pan, Cheng-Song You, Heng-Yu Wang et al. · 0 citations