Lower diameter bounds for compact shrinking Ricci solitons
58 citations recorded by the source corpus.
It is shown that the diameter of a compact shrinking Ricci soliton has a universal lower bound. This is proved by extending universal estimates for the first non-zero eigenvalue of Laplacian on compact Riemannian manifolds with lower Ricci curvature bound to a twisted Laplacian on compact shrinking Ricci solitons.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/054a9a4b66502595e8683a0818db585d8aa96ebe
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- 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]).”
- On second variation of Perelman’s Ricci shrinker entropy (2010, background): “Let u be a (non-constant) first eigenfunction so that Then by direct computations (see also [9]), we get Since u is non-constant, we obtain This completes the proof of Theorem 1.1.”
- Geometry of shrinking Ricci solitons (2014, background): “[14] A. Futaki and Y. Sano, Lower diameter bounds for compact shrinking Ricci solitons, Asian J. Math.”