4 fix

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).


 rt.representation-theory riemannian-geometry geometry 
 
 
3 fix formla

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).

2 deleted 64 characters in body; edited tags

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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