Symmetrization maps and minimal border rank Comon's conjecture

One of the fundamental open problems in the field of tensors is the border Comon's conjecture: given a symmetric tensor $F\in(\mathbb{C}^n)^{\otimes d}$ for $d\geq 3$, its border and symmetric border ranks are equal. In this paper, we prove the conjecture for large classes of concise tensors in $(\m