arXiv subjects

Shanlin Guan

Publications and source records attributed to Shanlin Guan.

3 recordsLinked to original sources

arXiv2026

Constant Chern holomorphic sectional curvature on two-step solvmanifolds

Let $M=Γ\backslash G$ be a compact solvmanifold with a left-invariant Hermitian structure whose Lie algebra is two-step solvable. If the Chern holomorphic sectional curvature is constant, then the derived algebra is $J$-invariant and the Chern connection is flat. At the Lie-algebra level, we also prove that constant Chern holomorphic sectional curvature is impossible for a unimodular two-step solvable Hermitian Lie algebra of mixed Freibert-Swann type.

math.DG↗

arXiv2026

Rigidity of Three-Dimensional Self-Shrinkers with Constant Norm of the Second Fundamental Form

Let $X:M^3\to\R^4$ be a complete, connected self-shrinker without boundary, and suppose that the squared norm $S$ of its second fundamental form is constant. We prove that $S=0$ or $S=1$. Accordingly, the image is a hyperplane through the origin or a generalized cylinder $\mathbb S^k(\sqrt{k})\times\R^{3-k}$, $1\le k\le3$, and the immersion is a Riemannian covering onto its image.

math.DG↗

arXiv2026

The Second Gap for Minimal Hypersurfaces in the Unit Sphere with Constant Cubic Trace

Let $M^n$, $n\ge3$, be a closed oriented minimal hypersurface in the unit sphere with constant scalar curvature and constant $f_3=\tr(h^3)$, where $h$ is the second fundamental form. We prove that $S=\norm h^2>n$ implies $S\ge2n$. Equality holds if and only if each connected component is locally congruent to a Cartan minimal isoparametric hypersurface with three distinct principal curvatures.

math.DG↗