Smoothing Of The Riemannian Metrics With Bounded Weak Norms

In this paper,we discuss the smoothing of the Riemannian metrics with uniformly bounded weak norms by embedding method.Based on the method of Petersen,Wei and Ye,that is,it is locally embedded in the Hilbert space to achieve the smoothness of the metric,and the sectional curvature of the smoothed metric is calculated specifically,and then discussing the smoothness of the smoothed metric.