论文标题
总平均曲率和第一个Dirac特征值
Total mean curvature and first Dirac eigenvalue
论文作者
论文摘要
在本说明中，我们证明了欧几里得空间中某些超曲面的第一个dirac特征值的最佳上限，这是通过结合正质量定理和准球形指标的构建。这是该估计值的直接结果，我们获得了狄拉克操作员在三维渐近平坦的歧管上的大球上的第一个特征值的渐近膨胀。我们还研究了三维riemannian歧管中的小测量球的扩展。我们最终讨论了如何适应该方法以在双曲线空间中产生相似的结果。
In this note, we prove an optimal upper bound for the first Dirac eigenvalue of some hypersurfaces in Euclidean space by combining a positive mass theorem and the construction of quasi-spherical metrics. As a direct consequence of this estimate, we obtain an asymptotic expansion for the first eigenvalue of the Dirac operator on large spheres in three dimensional asymptotically flat manifolds. We also study this expansion for small geodesic spheres in a three dimensional Riemannian manifold. We finally discuss how this method can be adapted to yield similar results in the hyperbolic space.
