https://neckpinch.com/authors/yan-li/New arXiv papers by Yan Li, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2103.06439/arxiv:2103.06439Thu, 11 Mar 2021 00:00:00 GMTYan Li, ZhenYe Li — Let G be a connected, complex reductive group. In this paper, we classify G× G-equivariant normal ℝ-test configurations of a polarized G-compactification. Then for ℚ-Fano G-compactifications, we express the H-invariant of its equivariant normal ℝ-test configurations in terms of the combinatory data. Based on, we compute the semistable limit of a K-unstable Fano G-compactification. As an application, we show that for the two K-unstable Fano SO₄(ℂ)-compactifications, the corresponding semistable limits are indeed the limit spaces of the normalized Kähler-Ricci flow.Ricci flowKähler–Ricci flowKähler geometryStability & uniquenessKähler–Einstein & K-stability https://neckpinch.com/papers/1908.10091/arxiv:1908.10091Tue, 27 Aug 2019 00:00:00 GMTYan Li — In this article we prove the existence of Kahler-Ricci solitons on smoothable, K-stable Q-Fano varieties. We also investigate the behavior of twisted Kahler-Ricci solitons in the Gromov-Hausdorff topology under this smoothing family.Ricci solitonsKähler–Ricci solitonsKähler geometryLimit spaces & RCDKähler–Einstein & K-stability https://neckpinch.com/papers/1807.09167/arxiv:1807.09167Tue, 24 Jul 2018 00:00:00 GMTYan Li, Gang Tian, Xiaohua Zhu — In this paper, we prove that any solution of Kähler-Ricci flow on a Fano compactification M of semisimple complex Lie group, is of type II, if M admits no Kähler-Einstein metrics. As an application, we found two Fano compactifications of SO₄(ℂ) and one Fano compactification of Sp₄(ℂ), on which the Kähler-Ricci flow will develop singularities of type II. To the authors' knowledge, these are the first examples of Ricci flow with singularities of type II on Fano manifolds in the literature.Ricci flowKähler–Ricci flowEinstein metricsSingularitiesKähler geometryHomogeneous spacesKähler–Einstein & K-stability https://neckpinch.com/papers/1712.07934/arxiv:1712.07934Thu, 21 Dec 2017 00:00:00 GMTYan Li, Xiaohua Zhu — In this paper, we introduce a class of Sasaki manifolds with a reductive G-group action, called G-Sasaki manifolds. By reducing K-energy to a functional defined on a class of convex functions on a moment polytope, we give a criterion for the properness of K-energy. In particular, we deduce a sufficient and necessary condition related to the polytope for the existence of transverse G-Sasaki Einstein metrics. A similar result is also obtained for transverse G-Sasaki Ricci solitons. As an application, we construct several examples of G-Sasaki Ricci solitons by an established openness theorem for transverse G-Sasaki Ricci solitons.Ricci solitonsEinstein metricsSasakian & contact geometry