1 citations · 2 across the 5 of their papers we have counts for
5 papers
Quantitative Maximal Diameter Rigidity of Positive Ricci Curvature
Tianyin Ren, Xiaochun Rong
In Riemannian geometry, the Cheng's maximal diameter rigidity theorem says that if a complete -manifold of Ricci curvature, , has the maximal…
Improved Spectral Cluster Bounds for Orthonormal Systems
Tianyi Ren, An Zhang
We improve Frank-Sabin's work concerning the spectral cluster bounds for orthonormal systems at , on the flat torus and spaces of nonpositive sectional curvature, by shri…
Resolvent Estimates for Schrödinger Operators with Potentials in Lebesgue Spaces
Tianyi Ren
We prove resolvent estimates in the Euclidean setting for Schrödinger operators with potentials in Lebesgue spaces: . The estimates were already obtained by…
Resolvent Estimate for the Sphere off the Line
Tianyi Ren
We extend the resolvent estimate on the sphere to exponents off the line . Since the condition on the exp…
An Endpoint Version of Uniform Sobolev Inequalities
Tianyi Ren, Yakun Xi, Cheng Zhang
We prove an endpoint version of the uniform Sobolev inequalities in Kenig-Ruiz-Sogge [8]. It was known that strong type inequalities no longer hold at the endpoints; however, we sh…