Monotone volume formulas for geometric flows
Monotone volume formulas for geometric flows
We consider a closed manifold M with a Riemannian metric gij(t) evolving by ∂tgij = –2Sij where Sij(t) is a symmetric two-tensor on (M, g(t)). We prove that if Sij satisfies the tensor inequality 𝒟(Sij, X) ≧ 0 for all vector fields X on M, where 𝒟(Sij, X) is defined …