= Weyl law
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{title2=$N(\lambda)\sim\omega_d\operatorname{Vol}(M)(2\pi)^{-d}\lambda^{d/2}$}
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For the positive scalar <Laplace-Beltrami operator> on a closed $d$-dimensional <Riemannian manifold>, the number of <eigenvalues> at most $\lambda$, counted with multiplicity, has the displayed leading asymptotic. The exponent determines the dimension and the coefficient determines the total volume of the <Riemannian metric>. There is an analogous result with fixed <Dirichlet boundary conditions> or <Neumann boundary conditions> on a compact smooth domain.
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