Zobrazeno 1 - 10
of 28
pro vyhledávání: '"Yan, Zetian"'
Autor:
Chern, Shane, Yan, Zetian
We prove Juhl type formulas for the curved Ovsienko--Redou operators and their linear analogues, which indicate the associated formal self-adjointness, thereby confirming two conjectures of Case, Lin, and Yuan. We also offer an extension of Juhl's or
Externí odkaz:
http://arxiv.org/abs/2407.12280
Autor:
Case, Jeffrey S., Yan, Zetian
We prove that the curved Ovsienko--Redou operators and a related family of differential operators are formally self-adjoint. This verifies two conjectures of Case, Lin, and Yuan.
Comment: 14 pages
Comment: 14 pages
Externí odkaz:
http://arxiv.org/abs/2405.09532
Autor:
Hong, Han, Yan, Zetian
We prove that the nonnegative $3$-intermediate Ricci curvature and uniformly positive $k$-triRic curvature implies rigidity of complete noncompact two-sided stable minimal hypersurfaces in a Riemannian manifold $(X^5,g)$ with bounded geometry. The no
Externí odkaz:
http://arxiv.org/abs/2405.06867
Autor:
Yan, Zetian
We prove that a stable $C^{1,1}$-to-edge properly embedded free boundary minimal hypersurface $\Sigma^3$ of a $4$-dimensional wedge domain $\Omega^4_{\theta}$ with angle $\theta\in (0,\pi]$ is flat.
Comment: Update the introduction and add some
Comment: Update the introduction and add some
Externí odkaz:
http://arxiv.org/abs/2403.08005
Autor:
Cho, Gunhee, Yan, Zetian
We establish a sharp Sobolev trace inequality on the Siegel domain $\Omega_{n+1}$ involving the weighted norm-$W^{2,2}(\Omega_{n+1}, \rho^{1-2[\gamma]})$. The inequality is closely related the realization of fractional powers of the sub-Laplacian on
Externí odkaz:
http://arxiv.org/abs/2304.06874
Autor:
Yan, Zetian
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 the existence and the classification of minimizers of the CR invariant S
Externí odkaz:
http://arxiv.org/abs/2301.07170
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 convergence rate of the Yamabe flow. Inspired by their result, we study
Externí odkaz:
http://arxiv.org/abs/2212.04367
Let $(M^n,g,e^{-\phi}dV_g,e^{-\phi}dA_g,m)$ be a compact smooth metric measure space with boundary with $n\geqslant 3$. In this article, we consider several Yamabe-type problems on a compact smooth metric measure space with or without boundary: uniqu
Externí odkaz:
http://arxiv.org/abs/2209.13892
We introduce a Yamabe-type flow \begin{align*} \left\{ \begin{array}{ll} \frac{\partial g}{\partial t} &=(r^m_{\phi}-R^m_{\phi})g \\ \frac{\partial \phi}{\partial t} &=\frac{m}{2}(R^m_{\phi}-r^m_{\phi}) \end{array} \right. ~~\mbox{ in }M ~~\mbox{ and
Externí odkaz:
http://arxiv.org/abs/2208.11310
Autor:
Yan, Zetian
We improve higher-order CR Sobolev inequalities on $S^{2n+1}$ under the vanishing of higher order moments of the volume element. As an application, we give a new and direct proof of the classification of minimizers of the CR invariant higher-order So
Externí odkaz:
http://arxiv.org/abs/2203.13873