Diffusion semigroup on manifolds with time-dependent metrics

摘要

Let L t := Δ t + Z t {L_{t}:=Delta_{t}+Z_{t}} , t ∈ [ 0 , T c ) {tin[0,T_{c})} on a differential manifold equipped with a complete geometric flow ( g t ) t ∈ [ 0 , T c ) {(g_{t})_{tin[0,T_{c})}} , where Δ t {Delta_{t}} is the Laplacian operator induced by the metric g t {g_{t}} and ( Z t ) t ∈ [ 0 , T c ) {(Z_{t})_{tin[0,T_{c})}} is a family of C 1