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



We prove a lower bound estimate for the first non-zero eigenvalue of the Witten–Laplacian on compact Riemannian manifolds. As an application, we derive a lower bound estimate for the diameter of compact gradient shrinking Ricci solitons. Our results improve some previous estimates which were obtained by the first author and Sano (Asian J Math, to appear), and by Andrews and Ni (Comm Partial Differential Equ, to appear). Moreover, we extend the diameter estimate to compact self-similar shrinkers of mean curvature flow.



Annals of Global Analysis and GeometrySpringer Journals

Published: Aug 1, 2013

DOI: 10.1007/s10455-012-9358-5

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