diff f0945ea..3ff9228 closed_ricci_flow_curvature_blowup_v2.txt
diff --git a/closed_ricci_flow_curvature_blowup_v2.txt b/closed_ricci_flow_curvature_blowup_v2.txt index d3da9b8..5f8275f 100644 --- a/closed_ricci_flow_curvature_blowup_v2.txt +++ b/closed_ricci_flow_curvature_blowup_v2.txt @@ -7,35 +7,8 @@ ================================================================================ -0. HOW TO READ THIS -Sections 1 to 3 need only calculus, vectors, and the idea of an average. They -contain the whole story: what is being asked, why the obvious guess is wrong, -and what the answer is. - -Sections 4 to 9 are the proof. Every step of the argument is stated. Most are -computations you can check by differentiating. A few use a standard tool from -analysis -- a heat kernel estimate, a maximum principle, Shi's derivative -estimate -- and each of those is named at the moment it is used, with the -precise place where it is proved. When this document says "imported", that is -exactly what it means: proved elsewhere, cited exactly, not re-proved here. -That is the only kind of gap in this document, and it is never hidden. - -Section 10 says honestly what is new and what is borrowed. Section 11 is a map -of which lemma feeds which. Section 12 is a glossary of every symbol. Section -13 is a list of things you can test yourself on. - -Two habits make the proof much easier to follow. - - (a) Almost every estimate below has the same shape: "something is at most a - constant times a power of r, or a power of delta". Watch the powers. The - powers are the plot. - - (b) There are exactly two length scales in the problem, sqrt(delta) and - theta, with theta much smaller. Almost every lemma says which of the two - it is about. Mixing them up is the main way to get lost. - 1. THE QUESTION