The Deturck's tricks
Date Issued
2010
Date
2010
Author(s)
Lin, Chien
Abstract
In this review, we would concentrate on two main results "Short-time existence of Ricci flow" and "Local existence of metrics with prescribed Ricci curvature". All of these materials could be found in the original papers by D.M. Deturck.([2],[3]) Both proofs depended on whether they''re strictly parabolic and elliptic, resp. Because θgθt= -2 Ricc(g) and Ricc''(g)h are not strictly parabolic and elliptic, we must modify the equations (i.e. adding some terms) to make them to satisfy the requirements. Without complete proofs we would just point out the key steps in Chapter 3 after giving some preliminaries.
Subjects
Ricci flow
Ricci curvature
strictly parabolic
elliptic
local solvability
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