Large m asymptotics for minimal partitions of the Dirichlet eigenvalue

In this paper, we study large m asymptotics of the l1 minimal m-partition problem for Dirichlet eigenvalue. For any smooth domain Ω ⊂ ℝn such that ∣Ω∣ = 1, prove limit $${\rm{lim}}_{m \to \infty}l_m^1\left(\Omega \right) {c_0}$$ exists, and constant c0 is independent shape Ω. Here, $$l_m^1\left({\rm{\Omega}} \right)$$ denotes value normalized sum first Laplacian eigenvalues