## Curvature Bounds, Obata Theorem, and Boundary Estimates for Dirichlet and Neumann Eignproblems. (arXiv:1803.04233v1 [math.DG])

We establish integral formulas and sharp two-sided bounds for the Ricci curvature, mean curvature and second fundamental form on a Riemannian manifold with boundary. As applications, the Lichnerowicz estimate and Obata theorem for the first eigenvalue, as well as sharp gradient/Hessian estimates on the boundary for eigenfunctions, are presented for the Dirichlet and Neumann eigenproblems.查看全文

## Solidot 文章翻译

 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 We establish integral formulas and sharp two-sided bounds for the Ricci curvature, mean curvature and second fundamental form on a Riemannian manifold with boundary. As applications, the Lichnerowicz estimate and Obata theorem for the first eigenvalue, as well as sharp gradient/Hessian estimates on the boundary for eigenfunctions, are presented for the Dirichlet and Neumann eigenproblems.