Title: A PDE approach to the construction of surfaces of minimum mean curvature variation

Speaker: Pablo Raúl Stinga, Iowa State University

Abstract: The construction of fair surfaces in computer-aided design (CAD) and computer-aided manufacturing (CAM) involves finding a minimizer of the quadratic tangential variation of the mean curvature of a surface. Despite their importance in applied problems, solutions have only been found through numerical schemes. We present two different analytical ways of constructing minimizers. These are the first rigorous results on the existence and regularity of surfaces of minimum mean curvature variation. This is joint work with Luis A. Caffarelli (The University of Texas at Austin) and Hernán Vivas (Universidad Nacional de Mar del Plata, Argentina).