https://neckpinch.com/authors/liang-zhang/New arXiv papers by Liang Zhang, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2112.02001/arxiv:2112.02001Fri, 03 Dec 2021 00:00:00 GMTLiang Zhang — In this paper, we extend Tosatti's method to study the lower boundedness of modified K-energy on a Fano manifold and apply this result to study the relative K-stability of the deformation space of a Kähler Ricci soliton.Ricci solitonsKähler–Ricci solitonsKähler geometryStability & uniqueness https://neckpinch.com/papers/2107.12680/arxiv:2107.12680Tue, 27 Jul 2021 00:00:00 GMTGang Tian, Liang Zhang, Xiaohua Zhu — Let (M,J₀) be a Fano manifold which admits a Kähler-Ricci soliton, we analyze the behavior of the Kähler-Ricci flow near this soliton as we deform the complex structure J₀. First, we will establish an inequality of Lojasiewicz's type for Perelman's entropy along the Kähler-Ricci flow. Then we prove the convergence of Kähler-Ricci flow when the complex structure associated to the initial value lies in the kernel Z or negative part of the second variation operator of Perelman's entropy. As applications, we solve the Yau-Tian-Donaldson conjecture for the existence of Kähler-Ricci solitons in the moduli space of complex structures near J₀, and we show that the kernel Z corresponds to the local moduli space of Fano manifolds which are modified K-semistable. We also prove an uniqueness theorem for Kähler-Ricci solitons.Ricci flowKähler–Ricci flowRicci solitonsKähler–Ricci solitonsPerelman entropyKähler geometryStability & uniquenessKähler–Einstein & K-stability