Some Notes on $k$-Minimality (Journal of Mathematical Study, 2019)
The concept of minimality is generalized in different ways, one of whichis the definition of $k$-minimality. In this paper $k$-minimality is studied for minimal hypersurfaces of a Euclidean space under different conditions on the number of principalcurvatures. We will also give a counterexample to $L_k$-conjecture.