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Inequalities between Dirichlet and Neumann eigenvalues on Carnot groups (2411.11168v1)
Published 17 Nov 2024 in math.AP and math.SP
Abstract: We show that the $j$-th Dirichlet eigenvalue of the sub-Laplacian on an open set of a Carnot group is greater than the $(j+1)$-st Neumann eigenvalue. This extends earlier results in the Euclidean and Heisenberg case and has a remarkably simple proof.
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