Abstract
In the present paper, we consider Dirichlet Laplacian on compact surface. We show that for a fixed surface with boundary X, a finite increasing sequence of real numbers 0<a1<a2<⋯<aN and a positive number A, there exists a metric g on X such that for any integer 1≤k≤N, we have λkD(X,g)=ak and Area(X,g)=A.
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