Mathematics · Fudan University
成浩轩
I study geometric and analytic questions on graphs and manifolds.
I joined the direct-entry PhD program in mathematics at Fudan University in 2025. Before joining Fudan, I studied mathematics at South China Normal University.
My main area is discrete geometric analysis, especially geometric structures on graphs, discrete curvature, and spectral questions related to discrete Einstein metrics. I also work on geometric analysis on manifolds, including volume growth, stochastic processes, and curvature flows.
Nine arXiv preprints in discrete geometry, curvature flows, geometric analysis, and surface theory.
Possible slopes of principal curvatures near umbilics and a classification of compact surfaces satisfying a cubic Weingarten relation.
Complete bounded-curvature manifolds in every dimension at least two with no Euclidean isometric immersion of bounded mean curvature.
Examples in every dimension at least four with nonnegative Ricci curvature and unbounded normalized scalar curvature integrals over expanding geodesic balls.
A construction of compact embedded rotational tori whose homothetic dilations solve odd σ_k-curvature flows in a Sobolev almost-everywhere sense.
A volume-growth condition that ensures recurrence for stable subordinations of Brownian motion on complete Riemannian manifolds.
An exact analysis of how subdividing an edge can decrease, preserve, or increase the largest eigenvalue of a tree Ricci matrix.
The limiting behavior and eventual monotonicity of the largest Ricci-matrix eigenvalue under repeated leaf attachment.
A classification of finite trees whose Lin--Lu--Yau discrete Einstein metric has positive curvature, together with the zero-curvature boundary.
Existence and uniqueness of Lin--Lu--Yau discrete Einstein metrics on trees via Perron--Frobenius theory, with spectral bounds and structural properties.
I build small systems to make long mathematical projects easier to resume, inspect, and verify.
I built this workbench to organize research in discrete geometry and geometric analysis with Codex. It keeps track of proof attempts, dependencies, and computational evidence so that I can resume a problem without losing its history. The public repository shares the framework and project templates.
View repositoryBeijing Institute of Mathematical Sciences and Applications (BIMSA)
Talk pageBeijing Institute of Mathematical Sciences and Applications (BIMSA)