The weighted conformal mean curvature flow

초록

We introduce a Yamabe-type flow R_φ^m = 0 in M and { ∂g/∂t = 2(h_φ^m - H_φ^m)g, ∂φ/∂t = m(H_φ^m - h_φ^m) } on ∂M on a smooth metric measure space with boundary (M, g, e^-φ dV_g, e^-φ dA_g, m), where R_φ^m is the weighted scalar curvature, H_φ^m is the weighted mean curvature and h_φ^m is the average of the weighted mean curvature. We prove the long-time existence and convergence of this flow.

키워드