Zobrazeno 1 - 10
of 76
pro vyhledávání: '"Chen, Xuezhang"'
Autor:
Chen, Xuezhang, Zhang, Shihong
We introduce the notion of a biharmonic Poisson kernel associated with certain pair of conformal boundary operators and present its explicit formula. With this powerful tool, we next establish the classification theorems of nonnegative solutions to a
Externí odkaz:
http://arxiv.org/abs/2406.10489
Autor:
Chen, Xuezhang, Wei, Wei
We establish the global $C^2$-estimates for the modified $\sigma_2$ curvature equation with prescribed boundary mean curvature, and particularly, the local boundary $C^2$ estimates on three-manifolds.
Comment: Comments welcome
Comment: Comments welcome
Externí odkaz:
http://arxiv.org/abs/2405.13134
Autor:
Chen, Xuezhang, Zhang, Shihong
We establish a fourth order sharp Sobolev trace inequality on three-balls, and its equivalence to a third order sharp Sobolev inequality on two-spheres.
Comment: 29 pages. Comments are welcome!
Comment: 29 pages. Comments are welcome!
Externí odkaz:
http://arxiv.org/abs/2403.00380
Autor:
Chen, Xuezhang, Shi, Yalong
We derive explicit representation formulae of Green functions for GJMS operators on $n$-spheres, including the fractional ones. These formulae have natural geometric interpretations concerning the extrinsic geometry of the round sphere. Conversely, w
Externí odkaz:
http://arxiv.org/abs/2401.02087
Constrained Moser-Trudinger-Onofri inequality and a uniqueness criterion for the mean field equation
Autor:
Chen, Xuezhang, Zhang, Shihong
We establish Moser-Trudinger-Onofri inequalities under constraint of a deviation of the second order moments from $0$, which serves as an intermediate one between Chang-Hang's inequalities under first and second order moments constraints. A threshold
Externí odkaz:
http://arxiv.org/abs/2309.04706
Autor:
Chen, Xuezhang, Wei, Wei
We first establish local $C^2$ estimates of solutions to the $\sigma_2$-curvature equation with nonlinear Neumann boundary condition. Then, under assumption that the background metric has nonnegative mean curvature on totally non-umbilic boundary, fo
Externí odkaz:
http://arxiv.org/abs/2307.13942
Publikováno v:
In Advances in Mathematics December 2024 459
Autor:
Jia, Wenyu, Lin, Xuan, Chen, Xuezhang, Li, Hongliang, Zhang, Xingru, Zhang, Yuzhuo, Chen, Yinsong, Wang, Bin, Chen, Xikang, Chen, Ju, Tian, Huaqin
Publikováno v:
In Journal of Ethnopharmacology 12 June 2024 327
We establish three families of Sobolev trace inequalities of orders two and four in the unit ball under higher order moments constraint, and are able to construct \emph{smooth} test functions to show all such inequalities are \emph{almost optimal}. S
Externí odkaz:
http://arxiv.org/abs/2107.08647
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 isoperimetric ratio over the scalar-flat conformal class is strictly l
Externí odkaz:
http://arxiv.org/abs/1910.01512