https://neckpinch.com/authors/shouhei-honda/New arXiv papers by Shouhei Honda, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2311.01342/arxiv:2311.01342Thu, 02 Nov 2023 00:00:00 GMTShouhei Honda, Christian Ketterer, Ilaria Mondello, Raquel Perales, Chiara Rigoni — We establish a nonlinear analogue of a splitting map into a Euclidean space, as a harmonic map into a flat torus. We prove that the existence of such a map implies Gromov-Hausdorff closeness to a flat torus in any dimension. Furthermore, Gromov-Hausdorff closeness to a flat torus and an integral bound on r_M(x), the smallest eigenvalue of the Ricci tensor ricₓ in x, imply the existence of a harmonic splitting map. Combining these results with Stern's inequality, we provide a new Gromov-Hausdorff stability theorem for flat 3-tori. The main tools we employ include the harmonic map heat flow, Ricci flow, and both Ricci limits and RCD theories.Ricci flowScalar curvatureLimit spaces & RCDStability & uniquenessHarmonic maps & DeTurck trickEigenvalues & spectrum