Jiahua Zou

collaborators

4 papers

math.DG2025

Index and nullity of minimal surface doublings, I

Nikolaos Kapouleas, Jiahua Zou

We prove that for any large enough $m \in N$ , the genus $I^^{3} = m + 1$ equator-poles minimal surface doubling of the equatorial two-sphere $I^£^{0} = S_{eq}^{2}$ in…

math.DG2025

Self-expanders of positive genus

Guanhua Shao, Jiahua Zou

For a general class of cones in $R^{3}$ , we construct self-expanders of positive genus asymptotic to these cones. As a result, we use these self-expanders to construct a mea…

math.DG2025

Self-shrinkers with any number of ends in $R^{3}$ by stacking $R^{2}$

Guanhua Shao, Jiahua Zou

For each half-integer $J$ and large enough integer $m$ we construct by PDE gluing methods a self-shrinker $M ˘ [J, m]$ with $2 J + 1$ ends and genus $2 J (m - 1)$ . $M ˘ [J, m]$ re…

math.DG2024

Minimal hypersurfaces in $S^{4} (1)$ by doubling the equatorial $S^{3}$

Nikolaos Kapouleas, Jiahua Zou

For each large enough $m \in N$ we construct by PDE gluing methods a closed embedded smooth minimal hypersurface $M ˘_{m}$ doubling the equatorial three-sphere $\mathb…

Index and nullity of minimal surface doublings, I

Self-expanders of positive genus

Self-shrinkers with any number of ends in R3 by stacking R2

Minimal hypersurfaces in S4(1) by doubling the equatorial S3

Self-shrinkers with any number of ends in $R^{3}$ by stacking $R^{2}$

Minimal hypersurfaces in $S^{4} (1)$ by doubling the equatorial $S^{3}$