Gongping Niu

Research

I am interested in geometric variational problems, regularity theory for geometric PDEs, and the singular behavior of geometric objects.

Preprints

• Isoperimetry of Singular CMC Hypersurfaces, 2026. arxiv

• A quantitative inequality for general area-minimizing hypercones, 2026. arxiv

• Generic Uniqueness of Isoperimetric Regions in Arbitrary Dimension, 2026. arxiv

• Strict Stability and Strict Minimality of Regular Area-Minimizing Hypercones: A Quantitative Characterization, 2026. arxiv

• Generic regularity of isoperimetric regions in dimension eight (with Kobe Marshall-Stevens and Davide Parise), 2025. arxiv

• Existence of singular isoperimetric regions, 2023. arxiv Note: This preprint contains an additional higher-dimensional generalization (Theorem 1.3 and Section 5)

Publications

• Isoperimetry by stretching (with Kobe Marshall-Stevens). International Mathematics Research Notices, 2026, rnag209. [DOI]

• Existence of singular isoperimetric regions in 8-dimensional manifolds. Calculus of Variations and Partial Differential Equations 63, 144 (2024). [DOI]

Teaching

Fall 2026

University of Rochester

• MATH 265 — Real Analysis I

• MATH 165 — Linear Algebra with Differential Equations

Spring 2026

University of Rochester

• MATH 282 — Introduction to Complex Analysis

• MATH 165 — Linear Algebra with Differential Equations