Riemannian metrics with prescribed volume and finite parts of Dirichlet spectrum

时   间：  2023-03-24 14:30 — 15:30

In 1980s  Colin de Verdiere proved that on any closed manifold of dimension at least 3, one can construct a smooth metric with arbitrarily prescribed finite parts of eigenvalues. Later on Lohkamp showed that one can further prescribe the volume. In this talk, I will explain how to extend their results to Dirichlet eigenvalues on manifolds with boundary. This is based on an ongoing joint work with He Xiang.