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- Title
PROPERTIES OF THE SOLUTIONS OF THE CONJUGATE HEAT EQUATIONS.
- Authors
Hamilton, Richard; Sesum, Natasa
- Abstract
Abstract. In this paper we consider the class A of those solutions u(x, t) to the conjugate heat equation ...u = -Δu + Ru on compact Kähler manifolds M with c[sub1] > () (where g(t) changes by the unnormalized Kähler Ricci flow, blowing up at T < ∞), which satisfy Perelman's differential Harnack inequality (6) on [0, T). We show A is nonempty. If ∣ Ric(g(t)) ∣ < ... which is always true if we have a type I singularity, we prove the solution u(x,t) satisfies the elliptic type Harnack inequality, with the constants that are uniform in time, If the flow g(1) has a type I singularity at T, then A has exactly one element.
- Subjects
HEAT equation; RICCI flow; MATHEMATICAL singularities; MATHEMATICAL analysis; BLOWING up (Algebraic geometry)
- Publication
American Journal of Mathematics, 2009, Vol 131, Issue 1, p153
- ISSN
0002-9327
- Publication type
Article
- DOI
10.1353/ajm.0.0038