### On L1-biharmonic hypersurfaces with constant mean curvature in the Lorentz-Minkowski space

#### Abstract

In this paper, we study isometrically immersed spacelike hypersurfaces in the Lorentz-

Minkowski space, whose position vector eld satises an extended version of biharmonicity

condition, named L1-biharmonicity, where L1 stands for the linearized operator of the rst variation

of the 2-th mean curvature arising from normal variations of Hypersurface. A well-known

conjecture of Bang-Yen Chen says that any biharmonic Euclidean submanifold is minimal. We

introduce and verify an advanced version of Chen's conjecture, replacing the Laplace operator

by L1. For any spacelike hypersurface, having assumed that Mn has three distinct principal

curvatures and constant ordinary mean curvature, we prove that it must be 1-maximal.

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