Bessel functions, heat kernel and the conical Kähler–Ricci flow

Following Donaldson's openness theorem on deforming a conical Kähler–Einstein metric, we prove a parabolic Schauder-type estimate with respect to conical metrics. As a corollary, we show that the conical Kähler–Ricci flow exists for short time. The key is to establish the relevant heat kernel estimates, where we use the Weber formula on Bessel function of the second kind and Carslaw's heat kernel representation in [8].