7 papers
On some new Ricci flow invariant curvature conditions
Yiyan Xu
We would like to study new Ricci flow invariant curvature conditions. Specifically, we provide quantitative evidence for an unpublished conjecture of Böhm and Wilking. As an applic…
Sharing tripartite nonlocality sequentially using only projective measurements
Yiyang Xu, Hao Sun, Fenzhuo Guo +2
Bell nonlocality is a valuable resource in quantum information processing tasks. Scientists are interested in whether a single entangled state can generate a long sequence of nonlo…
On some rigidity theorems of Q-curvature
Yiyan Xu, Shihong Zhang
In this paper, we investigate the rigidity of Q-curvature. Specifically, we consider a closed, oriented -dimensional () Riemannian manifold and prove the followi…
On the existence of geodesic connecting Lagrangian graphs in
Yiyan Xu
In this paper we show that two Lagrangian graphs over the torus in with large Lagrangian phase can be connected via Lipschitz continuous geodesic with respect to the…
A rigidity theorem for codimension one shrinking gradient Ricci solitons in
Pengfei Guan, Peng Lu, Yiyan Xu
We prove a splitting theorem for complete gradient Ricci soliton with nonnegative curvature and establish a rigidity theorem for codimension one complete shrinking gradient Ricci s…
Convergence of metrics under self - dual Weyl tensor and Scalar curvature bounds
Yiyan Xu
We establish a compactness theorem for the metrics with bounded self - dual Weyl tensor and Scalar curvature. The key step is to estimate the harmonic radius, w…
Regularity for Harmonic - Einstein Equation
Yiyan Xu
We establish a regularity theorem for the Harmonic - Einstein Equation. As a byproduct of the local regularity, we also have a compactness theorem on Harmonic - Einstein equation.…