Properties of the solutions of the conjugate heat equation
| dc.creator | Hamilton, Richard | |
| dc.creator | Sesum, Natasa | |
| dc.date | 2006-01-17 | |
| dc.date.accessioned | 2026-07-07T06:59:01Z | |
| dc.date.available | 2026-07-07T06:59:01Z | |
| dc.description | In this paper we consider the class $\mathcal{A}$ of those solutions $u(x,t)$ to the conjugate heat equation $\frac{d}{dt}u = -Δu + Ru$ on compact Kähler manifolds $M$ with $c_1 > 0$ (where $g(t)$ changes by the unnormalized Kähler 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. | |
| dc.identifier | https://arxiv.org/abs/math/0601415 | |
| dc.identifier | http://arxiv.org/abs/math/0601415 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107593 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C44 | |
| dc.title | Properties of the solutions of the conjugate heat equation | |
| dc.type | text |