Biharmonic rotational surfaces in the four-dimensional Euclidean space are minimal

Abstract

In this paper, we show that any biharmonic simple rotational surface in the four-dimensional Euclidean space is minimal. The proof is based on reducing the biharmonic equation to a system of ordinary differential equations for the profile curve and then excluding all possible non-minimal branches. This is a partial affirmative answer to Chen's conjecture.

16 pages