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Tim Carson
Tim Carson
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The type-I condition is that for some $C > 0$ we have $|Rm| < \frac{C}{T_{sing} -t}$ where $T_{sing} < \infty$ is specifically the supremum of times such that $|Rm|$ is bounded.

In the type-II case, it will turn out the $T$ you get from your ODE estimate must be smaller than $T_{sing}$. (Indeed, if you just try to get such a $T$ from basic ODE estimatesthis route, it will nearly always be smaller). When $T < T_{sing}$ the estimate you get will not work at the singular time.

The type-I condition is that for some $C > 0$ we have $|Rm| < \frac{C}{T_{sing} -t}$ where $T_{sing} < \infty$ is specifically the supremum of times such that $|Rm|$ is bounded.

In the type-II case, it will turn out the $T$ you get from your ODE estimate must be smaller than $T_{sing}$. (Indeed, if you just try to get such a $T$ from basic ODE estimates, it will nearly always be smaller).

The type-I condition is that for some $C > 0$ we have $|Rm| < \frac{C}{T_{sing} -t}$ where $T_{sing} < \infty$ is specifically the supremum of times such that $|Rm|$ is bounded.

In the type-II case, it will turn out the $T$ you get from your ODE estimate must be smaller than $T_{sing}$. (Indeed, if you just try to get such a $T$ from this route, it will nearly always be smaller). When $T < T_{sing}$ the estimate you get will not work at the singular time.

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Tim Carson
Tim Carson
  • 856
  • 7
  • 12

The type-I condition is that for some $C > 0$ we have $|Rm| < \frac{C}{T_{sing} -t}$ where $T_{sing} < \infty$ is specifically the supremum of times such that $|Rm|$ is bounded.

In the type-II case, it will turn out the $T$ you get from your ODE estimate must be smaller than $T_{sing}$. (Indeed, if you just try to get such a $T$ from basic ODE estimates, it will nearly always be smaller).