Work

Local Topology of Riemannian Manifolds with Lower Intermediate Ricci Curvature Bounds

Year: 2026

Type: preprint

Abstract: We prove a vanishing theorem for the local Betti numbers of closed, $n$-dimensional Riemannian manifolds with a lower volume bound, an upper diameter bound, and a lower intermediate Ricci curvature bound. This generalizes and interpolates between known results under lower sectional and Ricci curvature bounds. Moreover, the methods extend to open manifolds, yielding a corresponding vanishing theorem for the global Betti numbers.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.10268

Authors: Reiser, Philipp, Zarei, Masoumeh

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7212145031

Cites: 21

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Related to: 10