On compact quotients of stratified groups, the number of δ-deep nodal domains and coarse zero-set features of sums of sub-Laplacian eigenfunctions grows polynomially in the eigenvalue bound, with arbitrarily small exponent loss.
Arnold,The topology of real algebraic curves (works of I.G
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Coarse nodal counts on sub-Riemannian manifolds
On compact quotients of stratified groups, the number of δ-deep nodal domains and coarse zero-set features of sums of sub-Laplacian eigenfunctions grows polynomially in the eigenvalue bound, with arbitrarily small exponent loss.