Eigenvalue lower bounds and splitting for modified Ricci flow

Abstract

We prove sharp lower bounds for eigenvalues of the drift Laplacian for a modified Ricci flow. The modified Ricci flow is a system of coupled equations for a metric and weighted volume that plays an important role in Ricci flow. We will also show that there is a splitting theorem in the case of equality.

Keywords

• ricci flow
• geometric flows
• eigenvalue
• drift laplacian