4 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…
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…
Equivariant Morse theory for Lie algebra actions on Riemannian foliations
Yi Lin, Zuoqin Wang
We consider a transverse isometric action of a finite-dimensional Lie algebra on a Riemannian foliation. In this setting, we study equivariant Morse--Bott theory on t…