Graduate Singularity Formation and Breakdown Ricci Tensor

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The Ricci tensor experiences systematic failures in the Ricci flow equation, leading to the formation of singularities in finite time due to its non-linear nature. These singularities are classified as curvature singularities, where the curvature tensor's norm approaches infinity as the singular time is approached. Research identifies two types of singular breakdowns: Type I and Type II, with Type I singular points requiring the Riemannian curvature tensor to blow up at a specific rate. The discussion raises questions about whether this "blow-up" is an inherent physical necessity or a limitation of tensor calculus. The need for proper citations and references for the research mentioned is emphasized to validate the discussion.
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TL;DR
Ricci flow equation
The Ricci tensor fails systematically in the Ricci flow equation: "due to the highly non-linear nature of the Ricci flow equation, singularities form in finite time. These singularities are curvature singularities, which means that as one approaches the singular time the norm of the curvature tensor blows up to infinity".

Case Study: Type I and Type II Singularities:

Citing a research that identified two types of singular breakdowns: "Type I and Type II singular points" where "the Riemannian curvature tensor has to blow up at least at a Type I rate" and "the Ricci curvature must blow up near every singular point of a Ricci flow".

Is this "blow-up" a physical necessity or a limitation of our tensor calculus approach?
 
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Why did you post this in the relativity subforum?
 
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Alien101 said:
TL;DR Summary: Ricci flow equation
Your post includes several direct quotes. What is the source of these quotations?
 
Alien101 said:
Citing a research
What research? Please give a reference. Otherwise we don't have a valid basis for discussion.
 

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