Boundary Spectral Inequalities from Measurable Sets on $W^{2,\infty }$ manifolds and their applications

Lu Chen, Haolin Liu, Hongyu Liu

Let $(\mathcal{M},g)$ be a compact connected $W^{2,\infty }$ Riemannian manifold with nonempty boundary and a uniformly elliptic Lipschitz metric. We establish quantitative boundary…