7 papers
Sharp weighted CR trace Sobolev inequalities
Gunhee Cho, Zetian Yan
We establish a sharp Sobolev trace inequality on the Siegel domain involving the weighted norm-. The inequality is closely related the reali…
Improved Sobolev inequalities on CR shpere
Zetian Yan
We establish improved CR Sobolev inequalities on CR sphere under the vanishing of higher order moments of the volume element. As a direct application, we give a simpler proof of th…
Convergence rate of the weighted Yamabe flow
Pak Tung Ho, Jinwoo Shin, Zetian Yan
The weighted Yamabe flow was the geometric flow introduced to study the weighted Yamabe problem on smooth metric measure spaces. Carlotto, Chodosh and Rubinstein have studied the c…
Some results on the weighted Yamabe problem with or without boundary
Pak Tung Ho, Jinwoo Shin, Zetian Yan
Let be a compact smooth metric measure space with boundary with . In this article, we consider several Yamabe-type problems on a com…
The weighted Yamabe problem with boundary
Pak Tung Ho, Jinwoo Shin, Zetian Yan
We introduce a Yamabe-type flow \begin{align*} \left\{ \begin{array}{ll} \frac{\partial g}{\partial t} &=(r^m_ϕ-R^m_ϕ)g \\ \frac{\partial ϕ}{\partial t} &=\frac{m}{2}(R^m_ϕ-r^m_ϕ)…
Improved higher-order Sobolev inequalities on CR sphere
Zetian Yan
We improve higher-order CR Sobolev inequalities on under the vanishing of higher order moments of the volume element. As an application, we give a new and direct proof o…
Convergence of the Weighted Yamabe Flow
Zetian Yan
We introduce the weighted Yamabe flow , on a smooth metric measure space $(M^…