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What's the most natural way to establish the asymptotics of \Delta $\Delta$ on a compact Riemannian manifold M of dimension N? The asymptotics should be 

#(values $$\#\{v < A^2) A^2\} = const*vol(M)*A^n \mathrm{const}*\mathrm{vol}(M)*A^n + O(something)
o(\mathrm{something})$$
(Perhaps one could consider first a case of Kahler manifold? The Laplacian is partiularly simple there).
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What's the most natural way to establish the asymptotics of \Delta (the Laplacian \sum g_ij d/dx_i \wedge d/dx_j) on a compact Riemannian manifold M of dimension N. ? The asymptotics should be 

#(values < A^2) = const*vol(M)*A^n + O(something)

(Perhaps one could consider first a case of Kahler manifold? The Laplacian is partiularly simple there).
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What's the most natural way to establish the asymptotics of \Delta (the Laplacian \sum g_ij d/dx_i \wedge d/dx_j) on a compact Riemannian manifold M of dimension N. The asymptotics should be 

#(values < A^2) = const*vol(M)*A^n + O(something)

(shall we add tags quantum-mechanics and riemannian-geometry?)

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