5 papers
New Qualitative and Quantitative Estimates for Neumann Eigenvalues toward Pólya's Conjecture
Xiang He, Renjin Jiang, Fanghua Lin +1
We introduce the Enhanced Neumann Pólya inequality, which is stronger than Pólya's conjecture, and verify it for many classes of domains, including strip-tiling domains, Euclidean…
Short geodesics and multiplicities of eigenvalues of hyperbolic surfaces
Xiang He, Yunhui Wu, Haohao Zhang
In this paper, we obtain upper bounds on the multiplicity of Laplacian eigenvalues for closed hyperbolic surfaces in terms of the number of short closed geodesics and the genus …
Unsupervised learning of non-Abelian multi-gap topological phases
Xiangxu He, Ruo-Yang Zhang, Xiaohan Cui +2
Recent experiments have successfully realized multi-band non-Abelian topological insulators with parity-time symmetry. Their topological classification transcends the conventional…
Prescription of the Robin spectrum
Xiang He, Zuoqin Wang
Let be a compact connected smooth manifold with smooth boundary, and let be a positive continuous function on the boundary which is served as the Robin parameter. In this p…
Pólya's conjecture for thin products
Xiang He, Zuoqin Wang
Let be a bounded Euclidean domain. According to the famous Weyl law, both its Dirichlet eigenvalue and its Neumann eigenvalue have the same…