A Formula Relating Entropy Monotonicity to Harnack Inequalities
نویسنده
چکیده
∣ 2 u dV. This implies in particular that d dt μ(g(t), τ(t)) ≥ 0 with equality exactly for homothetically shrinking solutions of Ricci flow. An important consequence of this entropy formula is a lower volume ratio bound for solutions of Ricci flow on a closed manifold for a finite time interval [0, T ) asserting the existence of a constant κ > 0, only depending on n, T and g(0), such that the inequality Vt(B t r(x0)) rn+1 ≥ κ
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