On the first eigenvalue of the Witten–Laplacian and the diameter of compact shrinking solitons

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Eigenvalues of the drifted Laplacian on complete metric measure spaces (2013, background): “The authors of [2] stated, by constructing examples, that their estimates are sharp when Bakry-Émery Ricci tensor is not constant (see details in [8], [2] and [7]).”