区域的扰动：奇异黎曼流形
Perturbation of Domain: Singular Riemannian Manifolds
摘要：
研究了一类具有奇异度量的黎曼流形。特别地，我们研究了Dirichlet特征值的区域扰动问题，它依赖于Hardy不等式中的最佳常数。然而，我们表明，这些流形的常数是这样的，现有的定理不能应用，然后证明更好的估计，克服这一点。最后，我们建立了一个例子，可以用来证明我们的结果是最优的。完成这最后一步的方法包含在另一篇论文中更一般的颂歌设置中。
英文摘要：
We study a class of Riemannian manifolds which are equipped with a singular metric. In particular we study a domain perturbation problem for the Dirichlet eigenvalues which depends on the best constant in the Hardy Inequality. However, we show that for these manifolds the constant is such that existing theorems cannot be applied and then prove better estimates that overcome this. Finally we set up an example that can be used to show that our results are optimal. The methods for doing this final step are contained in another paper in a more general ode setting.
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。
