https://neckpinch.com/authors/shota-hamanaka/New arXiv papers by Shota Hamanaka, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2409.00583/arxiv:2409.00583Sun, 01 Sep 2024 00:00:00 GMTShota Hamanaka — We provide new type of decay estimate for scalar curvatures of steady gradient Ricci solitons. We also give certain upper bound for the diameter of a Riemannian manifold whose ∞-Bakry–Emery Ricci tensor is bounded by some positive constant from below. For the proofs, we use μ-bubbles introduced by Gromov.Ricci solitonsScalar curvatureLimit spaces & RCD https://neckpinch.com/papers/2208.01865/arxiv:2208.01865Wed, 03 Aug 2022 00:00:00 GMTShota Hamanaka — We study some preservation phenomena for lower bound of total scalar curvatures on a smooth manifold. In particular, we prove that the lower bound of the weighted total scalar curvature (which is known as Perelman's 𝓕-functional) on a closed n-manifold is preserved under the W^(1, p) (p > n²/2)-convergence of Riemannian metrics and uniformly C⁰-convergence of potential functions, provided that each scalar curvature is nonnegative. In the proof, we used a certain stability of the Ricci flow and the heat flow with the Ricci flow background. We also give some examples that may provide clues to identify the weakest topology for such a preservation phenomenon of the lower bound.Ricci flowScalar curvatureStability & uniqueness