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April 14, 2026Calculus of Variations and Partial Differential EquationsOpen Access

Volume estimates and convergence results for solutions to Ricci flow with L^p bounded scalar curvature

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Authors

JLJiawei LiuNanjing University of Science and TechnologyMSMiles SimonOtto-von-Guericke University Magdeburg

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Implication

Analytical study demonstrates convergence to an orbifold in 4-dimensional Ricci flow, suggesting extension of the flow time interval.

Key Points

  • The aim is to analyze the volume estimates and convergence behavior of n-dimensional Ricci flows with bounded scalar curvature.
  • Examined n-dimensional Ricci flows over a finite time interval [0, T)
  • Utilized estimates related to scalar curvature and Ricci curvature
  • Combined integral bounds from previous works to enhance understanding
  • Compared convergence behaviors specifically in four-dimensional cases
  • Non-collapsing estimates are confirmed for closed, four-dimensional manifolds
  • Showed that solutions converge to an orbifold as time approaches T
  • Proved that the Ricci flow can be extended beyond T using Orbifold Ricci flow
  • Local versions of the results were verified

Cite This Study

Liu et al. (2026) studied this question.

synapsesocial.com/papers/69ddd959e195c95cdefd69echttps://doi.org/10.1007/s00526-026-03314-4
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Also Consider

Synapse has enriched one closely related paper. Consider it for comparative context:

  1. 1Three-manifolds with positive Ricci curvature1982 · 3,037 citations