论文标题
cartan-hadamard歧管中的雷利型不平等现象
Reilly-type inequalities for submanifolds in Cartan-Hadamard manifolds
论文作者
论文摘要
令$ m $为$ m（\ ge2）$ - 尺寸封闭式的可定位子手机，在$ n $ dimensional完全连接的riemannian歧管$ n $中，$ n $的截面曲率以上是$δ$的。当$Δ<0 $，受NIU-XU的启发（ARXIV：2106.01912）时，我们分别为$ p $ -laplacian和$ l_t $ operator的第一个非零特征值提供了新的上限。这些概括了Niu-Xu的Laplacian（Arxiv：2106.01912）的工作，并改善了由于$ P $ -Laplacian和Grosjean和Grosjean和Grosjean和Grosjean（HokkaidoMath。J.，33（2）（233（2），33（2），33-3333339-33339，2004年，$ p $ -laplacian和grosjean（非线性肛门，196，111833，2020）引起的估计值。我们还为加权流形和一些边界价值问题获得了几种赖利型不平等。
Let $M$ be an $m (\ge2)$-dimensional closed orientable submanifold in an $n$-dimensional complete simply-connected Riemannian manifold $N$, where the sectional curvature of $N$ is bounded above by $δ$. When $δ<0$, inspired by Niu-Xu (arXiv:2106.01912), we give new upper bounds for the first nonzero eigenvalues of the $p$-Laplacian and the $L_T$ operator, respectively. These generalize Niu-Xu's work for the Laplacian (arXiv:2106.01912) and improve the estimates due to Chen (Nonlinear Anal.,196, 111833, 2020) for the $p$-Laplacian and Grosjean (Hokkaido Math. J., 33(2) , 319-339, 2004) for the $L_T$ operator, respectively. We also obtain several Reilly-type inequalities for the weighted manifolds and some boundary value problems.
