Another proof of the local curvature estimate for the Ricci flow

By using the De Giorgi iteration method we will give a new simple proof of the recent result of Kotschwar et al. (J Funct Anal 271(9):2604–2630, 2016) and Sesum (Am J Math 127(6):1315–1324, 2005) on the local boundedness of the Riemannian curvature tensor of solutions of Ricci flow in terms of its inital value on a given ball and a local uniform bound on the Ricci curvature.