Yukai Sun

activity

20202026

collaborators

6 papers

math.DG2026

Some rigidity theorems for spectral curvature bounds

Xiaoxiang Chai, Yukai Sun

We investigate the geometric implications of spectral curvature bounds, extending classical rigidity results in scalar curvature geometry to the spectral setting. By systematically…

math.DG2026

Warped area-minimizing hypersurface and warped product metric

Yukai Sun

Several metric splitting theorems under spectral Ricci curvature lower bounds have been established in recent years, yet the existing literature mostly yields only isometric direct…

math.DG2025

Gap phenomenon for scalar curvature

Yukai Sun, Changliang Wang

Inspired by Goette-Semmelmann \cite{GSSU2002}, we derive an estimate for the scalar curvature without a nonnegativity assumption on curvature operator. As an application, we show t…

math.DG2024

Positive scalar curvature and isolated conical singularity

Xianzhe Dai, Yukai Sun, Changliang Wang

We prove a Geroch type result for isolated conical singularity. Namely, we show that there is no Riemannian metric $g$ on $X # T^{n}$ with an isolated conical singularity which ha…

math.DG2022

Compacitification and positive mass theorem for fibered Euclidean end

Xianzhe Dai, Yukai Sun

In this note, we consider the positive mass theorem for Riemannian manifolds $(M^{n}, g)$ asymptotic to $(R^{k} \times X^{n - k}, g_{R^{k}} + g_{X})$ for $k \geq 3$ by s…

math.DG2020

Gromov Rigidity of Bi-Invariant Metrics on Lie Groups and Homogeneous Spaces

Yukai Sun, Xianzhe Dai

Gromov asked if the bi-invariant metrics on a compact Lie group are extremal compared to any other metrics. In this note, we prove that the bi-invariant metrics on a compact connec…