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Curvature integral on convex hypersurfaces
Qixuan Hu, Shuai Zhang
Let , , be the smooth, connected, complete, noncompact boundary of a closed convex set with nonempty interior in . We prove that its normalized scalar…
Scalar curvature growth on nonnegatively curved three-manifolds
Qixuan Hu
Let be a complete, connected, noncompact Riemannian three-manifold without boundary and with nonnegative sectional curvature. We prove that its scalar-curvature integral…
Some aspects of Cheng-Yau gradient estimates
Qixuan Hu, Chengjie Yu
In this note, we extend the rigidity of Cheng-Yau gradient estimate in \cite{HXY} to surfaces with lower Ricci curvature bound. Motivated by these sharp Cheng-Yau gradient estimate…
The rigidity and stability of gradient estimates
Qixuan Hu, Guoyi Xu, Chengjie Yu
In this note, we obtain the rigidity of the sharp Cheng-Yau gradient estimate for positive harmonic functions on surfaces with nonegative Gaussian curvature, the rigidity of the sh…