论文标题
第一个边界狄拉克特征值和边界容量电位
First boundary Dirac eigenvalue and boundary capacity potential
论文作者
论文摘要
我们为定向超出表面$σ$ dirac操作员的第一个特征值得出了新的下限，该dirac operator在毫无疑问的毫无疑问的扁平歧管（M n，g）中以非负标量曲线为旋转的非伴随域。这些边界涉及边界容量潜力，在某些情况下，（m n，g）的$σ$的容量产生了几种新的几何不等度。我们主要结果的证明依赖于对紧凑型riemannian旋转歧管边界的第一个特征值的估计值，并具有一个可能具有独立兴趣的单数度量。
We derive new lower bounds for the first eigenvalue of the Dirac operator of an oriented hypersurface $Σ$ bounding a noncompact domain in a spin asymptotically flat manifold (M n , g) with nonnegative scalar curvature. These bounds involve the boundary capacity potential and, in some cases, the capacity of $Σ$ in (M n , g) yielding several new geometric inequalities. The proof of our main result relies on an estimate for the first eigenvalue of the Dirac operator of boundaries of compact Riemannian spin manifolds endowed with a singular metric which may have independent interest.
