Twisted and conical Kähler–Ricci solitons on Fano manifolds

In this paper, we first study the relationship between the existence of twisted Kähler–Ricci solitons and the properness of modified twisted K-energy. Approximating by a sequence of smooth twisted Kähler–Ricci solitons, we obtain an existence result of conical Kähler–Ricci solitons.