扰动双调和算子通过共形变换度量的本质自伴性
Essential self-adjointness of perturbed biharmonic operators via conformally transformed metrics
摘要：
在附加的假设条件下，如下半有界里奇曲率或有界截面曲率，给出了作用在黎曼流形上Hermite向量丛截面上的扰动双调和算子的本质自伴性的充分条件.在下半有界里奇曲率的情况下，我们制定我们的结果的完整性的度量是共形的原始的，通过共形因子，取决于一个次要的扰动潜力$V$。在有界截面曲率的情况下，我们能够放松增长条件的副项的$V$强加在早期的文章。在这种情况下，我们的增长条件的$V$的副项是一致的文献中的自伴扰动双调和算子上$\mathbb{R}^n$。
英文摘要：
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 $\mathbb{R}^n$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
