https://neckpinch.com/authors/robin-neumayer/New arXiv papers by Robin Neumayer, from Neckpinch Tue, 03 Nov 2026 07:43:57 GMT https://neckpinch.com/papers/2210.16852/arxiv:2210.16852Sun, 30 Oct 2022 00:00:00 GMTRobin Neumayer — Examples show that Riemannian manifolds with almost-Euclidean lower bounds on scalar curvature and Perelman entropy need not be close to Euclidean space in any metric space sense. Here we show that if one additionally assumes an almost-Euclidean upper bound on volumes of geodesic balls, then unit balls in such a space are Gromov-Hausdorff close, and in fact bi-Hölder and bi-W^(1,p) homeomorphic, to Euclidean balls. We prove a compactness and limit space structure theorem under the same assumptions.Perelman entropyScalar curvatureLimit spaces & RCD