https://neckpinch.com/authors/yingying-zhang/New arXiv papers by Yingying Zhang, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2210.15627/arxiv:2210.15627Thu, 27 Oct 2022 00:00:00 GMTHuai-Dong Cao, Xiaofeng Sun, Yingying Zhang — In this paper we define a Weil-Petersson type metric on the space of shrinking Kaehler-Ricci solitons and prove a necessary and sufficient condition on when it is independent of the choices of Kaehler-Ricci soliton metrics. We also show that the Weil-Petersson metric is Kaehler when it defines a metric on the Kuranishi space of small deformations of Fano Kaehler-Ricci solitons. Finally, we establish the first and second order deformation of Fano Kähler-Ricci solitons and show that, essentially, the first effective term in deforming Kaehler-Ricci solitons leads to the Weil-Petersson metric.Ricci solitonsKähler–Ricci solitonsKähler geometry