论文标题
通过共同变换的指标，扰动的双旋转操作员的基本自我相关性
Essential self-adjointness of perturbed biharmonic operators via conformally transformed metrics
论文作者
论文摘要
我们为作用于遗传学载体束的扰动的双旋转算子的基本自我相互接合提供了足够的条件，并在riemannian歧管上具有其他假设，例如较低的半结合RICCI曲率或有界的分段曲率。在半结合的RICCI曲率的情况下，我们通过依赖于扰动潜在$ V $的少数人的保形因子来制定与原始曲率的度量的完整性。在有限的截面曲率情况下，我们能够放松较早文章中征收的$ v $的少数人的生长状况。在这种情况下，我们对$ v $的少数人的成长状况与$ \ mathbb {r}^n $上扰动的Biharmonic运算符的自我相关性的文献一致。
We give sufficient conditions for the essential self-adjointness of perturbed biharmonic operators acting on sections of a Hermitian vector bundle over a Riemannian manifold with additional assumptions, such as lower semi-bounded Ricci curvature or bounded sectional curvature. In the case of lower semi-bounded Ricci curvature, we formulate our results in terms of the completeness of the metric that is conformal to the original one, via a conformal factor that depends on a minorant of the perturbing potential $V$. In the bounded sectional curvature situation, we are able to relax the growth condition on the minorant of $V$ imposed in an earlier article. In this context, our growth condition on the minorant of $V$ is consistent with the literature on the self-adjointness of perturbed biharmonic operators on $\mathbb{R}^n$.
