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math.DG2023
Riemannian metrics with prescribed volume and finite parts of Dirichlet spectrum
Xiang He, Zuoqin Wang
In this paper we study the problem of prescribing Dirichlet eigenvalues on an arbitrary compact manifold of dimension with a non-empty smooth boundary . W…
math.DG2023
Prescription of finite Dirichlet eigenvalues and area on surface with boundary
Xiang He
In the present paper, we consider Dirichlet Laplacian on compact surface. We show that for a fixed surface with boundary , a finite increasing sequence of real numbers $0<a_1<a_…