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February 17, 2026Mathematische AnnalenOpen Access

On manifolds with almost non-negative Ricci curvature and integrally-positive k^th-scalar curvature

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Authors

ACAlessandro CucinottaAMAndrea Mondino

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Overview

This research demonstrates topological restrictions in manifolds with positive curvature conditions, implying geometric insights.

Key Points

  • The aim is to explore the implications of almost non-negative Ricci curvature and positive integral bounds on scalar curvature in manifolds.
  • Analyze Riemannian manifolds with specified curvature properties.
  • Determine dimensional behaviors at large scales for varying k values.
  • Establish connections between curvature conditions and topological features.
  • Manifolds have controlled local structures near 1-dimensional sub-manifolds.
  • Found upper bounds on first Betti number and volume growth is at most linear.
  • For k=n, dimension drop can improve under additional Ricci curvature conditions.

Cite This Study

Cucinotta et al. (2026) studied this question.

synapsesocial.com/papers/699405bb4e9c9e835dfd69d7https://doi.org/10.1007/s00208-026-03406-8
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