Gongping Niu

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20172026

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math.DG2026

A quantitative inequality for general area-minimizing hypercones

Gongping Niu

Let $C = \partial E \subset R^{n + 1}$ be an area-minimizing hypercone. The cone may have nonisolated singularities. We prove that there is a constant $c_{\mathbf{C}}>0…

math.DG2026

Generic Uniqueness of Isoperimetric Regions in Arbitrary Dimension

Gongping Niu

Let $M^{n + 1}$ be a closed, connected smooth manifold, where $n \geq 1$ . For each prescribed volume fraction $s \in (0, 1) ∖ {\frac{1}{2}}$ , we prove that the isoperimetric region o…

math.DG2026

Strict Stability and Strict Minimality of Regular Area-Minimizing Hypercones: A Quantitative Characterization

Gongping Niu

Let $C = \partial E \subset R^{n + 1}$ be a regular area-minimizing hypercone. We first prove that $C$ is simultaneously strictly stable and strictly minimizi…

math.DG2026

Isoperimetry by stretching

Kobe Marshall-Stevens, Gongping Niu

We construct isoperimetric regions from separating hypersurfaces in closed manifolds. This yields isoperimetric boundaries exhibiting a wide variety of topological types and singul…

math.DG2025

Generic regularity of isoperimetric regions in dimension eight

Kobe Marshall-Stevens, Gongping Niu, Davide Parise

We establish generic regularity results for isoperimetric regions in closed Riemannian manifolds of dimension eight. In particular, we show that every isoperimetric region has a sm…

math.DG2023

Existence of singular isoperimetric regions

Gongping Niu

It is well known that isoperimetric regions in a smooth compact $(n + 1)$ -manifold are smooth, up to a closed set of codimension at most $6$ . In this note, we first construct an $8$ -…