学术报告（王作勤 5.26）

摘要： 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 survey related known results and 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.