Ninth MSU-UAB Conference on Differential Equations and Computational Simulations. Electron. J. Diff. Eqns., Conference 20 (2013), pp. 151-164. Title: Real analytic solutions for the Willmore flow Author: Yuanzhen Shao (Vanderbilt Univ., Nashville, TN, USA) Abstract: In this article, we present a regularity result for the Willmore flow. This is obtained by using a truncated translation technique in conjunction with the implicit function theorem. Published October 31, 2013. Math Subject Classifications: 35B65, 35K55, 53A05, 53C44, 58J99. Key Words: Real analytic solution; Willmore flow; mean curvature; geometric evolution equation; implicit function theorem; maximal regularity.