Heat Kernel coupled with geometric flow, and Ricci flow

Koléhè Abdoulaye Coulibaly-Pasquier (1)

1 IECL - Institut Élie Cartan de Lorraine

We prove on-diagonal upper bound for the minimal fundamental solution of the heat equation evolving under geometric flow. In the case of Ricci flow, with non-negative Ricci curvature and a condition on the growth of volume of ball for the initial manifold, we derive Gaussian bounds for the minimal fundamental solution of the heat equation, and then for the conjugate heat equation.

Mots clés: Harnack inegality; Gaussian heat kernel estimate; Girsanov's; Ricci flow

Domaines: Probabilités [math.PR]; Géométrie différentielle [math.DG]

Koléhè Abdoulaye Coulibaly-Pasquier. Heat Kernel coupled with geometric flow, and Ricci flow. Séminaire de Probabilités, 2019, L, pp.221-256. ⟨10.1007/978-3-030-28535-7_11⟩. ⟨hal-00767995v2⟩