Yuping Ruan

activity

20182022

collaborators

4 papers

math.DG2022

The Cayley hyperbolic space and volume entropy rigidity

Yuping Ruan

Let $M$ be a Riemannian manifold with dimension greater or equal to $3$ which admits a complete, finite-volume Riemannian metric $g_{0}$ locally isometric to a rank-1 symmetric space…

math.DG2022

Filling volume minimality and boundary rigidity of metrics close to a negatively curved symmetric metric

Yuping Ruan

This paper generalizes D. Burago and S. Ivanov's work on filling volume minimality and boundary rigidity of almost real hyperbolic metrics. We show that regions with metrics close…

math.DG2019

An existence theorem on the isoperimetric ratio over scalar-flat conformal classes

Xuezhang Chen, Tianling Jin, Yuping Ruan

Let $(M, g)$ be a smooth compact Riemannian manifold of dimension $n$ with smooth boundary $\partial M$ , admitting a scalar-flat conformal metric. We prove that the supremum of the…

math.DG2018

The Han-Li conjecture in constant scalar curvature and constant boundary mean curvature problem on compact manifolds

Xuezhang Chen, Yuping Ruan, Liming Sun

The Han-Li conjecture states that: Let $(M, g_{0})$ be an $n$ -dimensional $(n \geq 3)$ smooth compact Riemannian manifold with boundary having positive (generalized) Yamabe constant an…