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- W2949897211 abstract "In this paper we consider the class $mathcal{A}$ of those solutions $u(x,t)$ to the conjugate heat equation $frac{d}{dt}u = -Delta u + Ru$ on compact Kahler manifolds $M$ with $c_1 > 0$ (where $g(t)$ changes by the unnormalized Kahler Ricci flow, blowing up at $T < infty$), which satisfy Perelman's differential Harnack inequality on $[0,T)$. We show $mathcal{A}$ is nonempty. If $|ric(g(t))| le frac{C}{T-t}$, which is alaways true if we have type I singularity, we prove the solution $u(x,t)$ satisfies the elliptic type Harnack inequlity, with the constants that are uniform in time. If the flow $g(t)$ has a type I singularity at $T$, then $mathcal{A}$ has excatly one element." @default.
- W2949897211 created "2019-06-27" @default.
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- W2949897211 date "2006-01-17" @default.
- W2949897211 modified "2023-10-16" @default.
- W2949897211 title "Properties of the solutions of the conjugate heat equation" @default.
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