https://neckpinch.com/authors/benedito-leandro/New arXiv papers by Benedito Leandro, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2210.01945arxiv:2210.01945Tue, 04 Oct 2022 00:00:00 GMTBenedito Leandro, Jeferson Poveda — In this paper, we prove some rigidity results for both shrinking and expanding Ricci solitons. First, we prove that compact shrinking Ricci solitons are Einstein if we control the maximum value of the potential function. Then, we prove some rigidity results for non-compact gradient expanding and shrinking Ricci solitons with pinched Ricci and scalar curvatures, assuming an asymptotic condition on the scalar curvature at infinity.Ricci solitonsScalar curvatureStability & uniquenessBoundaries & non-compact https://arxiv.org/abs/2207.04259arxiv:2207.04259Sat, 09 Jul 2022 00:00:00 GMTBenedito Leandro, Jeferson Poveda — We prove that a steady gradient Ricci soliton is either Ricci flat with a constant potential function or a quotient of the product steady soliton Nⁿ⁻¹×ℝ, where Nⁿ⁻¹ is Ricci flat, or isometric to the Bryant soliton (up to scalings), provided that a couple of geometric conditions inspired by the cigar soliton hold. As an application, we prove that any complete non-compact steady Ricci soliton with positive Ricci curvature controlled by the scalar curvature R, curvature tensor Rm satisfying |Rm|r→ o(1) and R→∞, as r→∞, must be the Bryant soliton. Moreover, we prove that any complete steady soliton with positively pinched Ricci curvature must be Ricci flat.Ricci solitonsAncient solutionsRicci-flat & Calabi–YauScalar curvatureBoundaries & non-compact https://arxiv.org/abs/2204.06678arxiv:2204.06678Thu, 14 Apr 2022 00:00:00 GMTHiuri dos Reis, Benedito Leandro, Rafael Novais — We present a characterization for the rotational soliton for the curve shortening flow (CSF) on the revolution surfaces of ℝ³. Furthermore, we describe the behavior of such curves by showing that the two ends of each open curve are asymptotic to a parallel geodesic.Curve shorteningSurfaces