Author

Zi-Hao Wang

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Preprint Sep 2026

Finite index constant mean curvature hypersurfaces in space forms of dimension at most seven

We study complete two-sided constant-mean-curvature hypersurfaces of dimensions $2\le n\le6$ and finite Morse index in simply connected space forms. In the round sphere the immersed domain is compact; in Euclidean space every noncompact example is minimal; in hyperbolic space of curvature $-1$ we obtain compactness und...

Zi-Hao Wang · 2 citations

Preprint Sep 2026

Minimality and Nonlinear Spectral Rigidity of Hypersurfaces in Real Space Forms

We study nonlinear mean-curvature spectral equations for hypersurfaces in Euclidean, spherical and hyperbolic space. For an admissible analytic response $F$ and ambient sectional curvature $c$, we prove minimality when the spectral parameter satisfies $\sigma\ge nc$, and strict mean-curvature bounds at gradient points...

Zi-Hao Wang · 0 citations

Preprint Sep 2026

Strongly stable CMC-one hypersurfaces in every hyperbolic space of dimension at least four

For every integer $d\ge4$, we prove strong stability for a subfamily of classical rotational hypersurfaces in $\mathbb H^d$ with normalized mean curvature one. The examples are complete, two-sided, properly embedded, and nowhere umbilic, with topology $\mathbb {R}\times\mathbb{S}^{d-2}$. An explicit positive supersolut...

Zi-Hao Wang · 1 citation