https://neckpinch.com/authors/bin-shen/New arXiv papers by Bin Shen, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.29796arxiv:2610.29796Wed, 21 Oct 2026 00:00:00 GMTBin Shen, Hui Zhang — Let an isometric involution act on a smooth Riemannian 3-sphere with sectional curvature at least one. We prove that every one-dimensional connected component of its fixed-point set has length at most 2π, and that the bound is sharp. The proof realizes the fixed circle as the link of a complete totally geodesic surface in a positively curved expanding Ricci soliton and applies Bishop–Gromov comparison to its area growth. The analytic input is an equivariant version of Deruelle's smoothing of positively curved cones. We use Gianniotis–Schulze's equivariant local deformation and explain a marked compactness argument for arbitrary finite isotropy. In particular, the end chart retains the specified group action, rather than only an unspecified conjugate.Ricci solitonsLimit spaces & RCD https://arxiv.org/abs/2501.01970arxiv:2501.01970Sun, 22 Dec 2024 00:00:00 GMTBin Shen — This manuscript investigates the curvature and topological properties of certain ∞-Einstein Finsler metrics on Finsler metric measure spaces. By imposing symmetry conditions, we construct a series of special metrics and analyze their equivalence on special manifolds. Provided a Ricci curvature bound, we establish a linear growth lower bound estimate for the S-curvature and the distortion, revealing the interplay between curvature and measure on ∞-Einstein Finsler manifolds. Furthermore, by introducing scalar curvature and imposing a linear growth lower bound condition, we derive upper and lower bounds for the distortion, S-curvature, and the scalar curvature itself on asymmetric essential gradient Ricci solitons with certain non-Riemannian curvature constraints. These results yield direct topological finiteness conclusions for some forward-complete ∞-Einstein Finsler manifolds. Our work partially addresses Gromov's conjecture of scalar curvature in the context of Finsler metric measure spaces and provides a foundation for further research in geometric analysis within general Finsler geometry.Ricci solitonsScalar curvatureLimit spaces & RCD https://arxiv.org/abs/2402.00006arxiv:2402.00006Thu, 14 Dec 2023 00:00:00 GMTBin Shen, Yuhan Zhu — In this paper, we explore the positive solutions to the Finslerian nonlinear equation ∂u/∂t = Δ^(∇u) u + aulog u + bu, which is related to Ricci solitons and serves as the Euler-Lagrange equation to the Finslerian log-energy functional. We then obtain the global gradient estimate of its positive solution on a compact Finsler metric measure space with the weighted Ricci curvature bounded below. Furthermore, using a new comparison theorem developed by the first author, we also establish a local gradient estimate on a non-compact forward complete Finsler metric measure spaces with the mixed weighted Ricci curvature bounded below, as well as finite bounds of misalignment and some non-Riemannian curvatures. Lastly, we prove the Harnack inequalities and a Liouville-type theorem of such solutions.Ricci solitonsHarnack inequalitiesLimit spaces & RCDBoundaries & non-compact