Stochastic proof of upper bound for the heat kernel coupled with geometric flow, and Ricci flow

Koléhé Abdoulaye Coulibaly-Pasquier (1)

1 IECN - Institut Élie Cartan de Nancy

We give a proof of Gaussian upper bound for the heat kernel coupled with the Ricci ow. Previous proofs by Lei Ni [5] use Harnack inequality and doubling volume property, also the recent proof by Zhang and Cao [6] uses Sobolev type inequality that is conserved along Ricci ow. We will use a horizontal coupling of curve [1] Arnaudon Thalmaier, C. , in order to generalize Harnack inequality with power -for inhomogeneous heat equation - introduced by F.Y Wang. In the case of Ricci ow, we will derive on-diagonal bound of the Heat kernel along Ricci ow ( and also for the usual Heat kernel on complete Manifold).

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

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

Koléhé Abdoulaye Coulibaly-Pasquier. Stochastic proof of upper bound for the heat kernel coupled with geometric flow, and Ricci flow. 2012. ⟨hal-00767995v1⟩