Long-time existence of some geometric flows with bounded scalar curvature

Key Points

• This survey aims to explore the behavior of scalar curvature during specific geometric flows.
• Analyzed the behavior of scalar curvature under Ricci flow.
• Examined Kähler-Ricci flow coupled with (1, 1)-forms.
• Investigated Laplacian flow.
• Identified properties of scalar curvature under different geometric flow conditions.
• Revealed the complexities of singularity formation.
• Provided insights into the long-time existence of these flows.