arXiv subjects

Jingyang Zhong

Publications and source records attributed to Jingyang Zhong.

3 recordsLinked to original sources

arXiv2026

Comparison of total quotient curvature

In this paper, we establish some comparison theorems for the total quotient curvature. Specifically, we examine the behavior of the functional with respect to the total quotient curvature and prove that the background Einstein metric achieves a sharp bound on the total quotient curvature. We prove that if the quotient curvature satisfies a point-wise lower (or upper) bound relative to the Einstein metric, then the corresponding integral inequality holds. Also we can show characterize the equality case. Our result generalizes the volume comparison theorem for scalar curvature and the rigidity results for $σ_k$-curvature.

math.DG↗

arXiv2023

Volume comparison theorem with respect to sigma-2 curvature

In this paper, we investigate the volume comparison theorem related to $σ_2$-curvature. In particular, we show that volume comparison theorem with respect to $σ_2$-curvature holds for metrics close to strictly stable positive Einstein metrics. By applying similar techniques, we derive the local rigidity theorem for strictly stable Ricci flat manifolds with respect to $σ_2$-curvature, which shows it admits no metric with positive $σ_2$-curvature near strictly stable Ricci-flat metrics.

math.DG↗

arXiv2016

Scalar Invariants of surfaces in conformal 3-sphere via Minkowski spacetime

For a surface in 3-sphere, by identifying the conformal round 3-sphere as the projectivized positive light cone in Minkowski 5-spacetime, we use the conformal Gauss map and the conformal transform to construct the associate homogeneous 4-surface in Minkowski 5-spacetime. We then derive the local fundamental theorem for a surface in conformal round 3-sphere from that of the associate 4-surface in Minkowski 5-spacetime. More importantly, following the idea of Fefferman and Graham, we construct local scalar invariants for a surface in conformal round 3-sphere. One distinct feature of our construction is to link the classic work of Blaschke to the works of Bryan and Fefferman-Graham.

math.DG↗