论文标题
在伊曼尼亚歧管上以异位浸入欧几里得空间中的一类椭圆形差分运算符的特征值估计值
Eigenvalue estimates for a class of elliptic differential operators in divergence form on Riemannian manifolds isometrically immersed in Euclidean space
论文作者
论文摘要
在本文中，我们在完整的riemannian歧管中以等异光浸入欧几里得空间中的有界域的形式获得了较大类别的椭圆形差分运算符的特征值估计。作为一种应用，我们给出了高斯孤子的特征值估计值，我们找到了一个域，使这些估计值的行为与laplacian情况的估计值相似。此外，我们还回答了Pólya的广义猜想。
In this paper, we obtain eigenvalue estimates for a larger class of elliptic differential operators in divergence form on a bounded domain in a complete Riemannian manifold isometrically immersed in Euclidean space. As an application, we give eigenvalue estimates in the Gaussian shrinking soliton, and we find a domain that makes the behavior of these estimates similar to the estimates for the case of the Laplacian. Moreover, we also give an answer to the generalized conjecture of Pólya.
