https://neckpinch.com/authors/junhao-tian/New arXiv papers by Junhao Tian, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2610.34340/arxiv:2610.34340Sun, 25 Oct 2026 00:00:00 GMTJunhao Tian, Kai Zheng — In this paper, we prove the long time existence of the pseudo-Calabi flow on a compact toric variety for any Tⁿ-invariant initial Kähler metric. If the Mabuchi functional is proper modulo automorphisms, the flow converges exponentially to a constant scalar curvature Kähler (cscK) metric. In particular, this gives a flow proof that properness of the K-energy implies the existence of a cscK metric in the toric setting.Other curvature flowsKähler geometryScalar curvatureLong-time existence & convergenceKähler–Einstein & K-stability https://neckpinch.com/papers/2603.19405/arxiv:2603.19405Thu, 19 Mar 2026 00:00:00 GMTJingrui Cheng, Junhao Tian — In this paper, we observe that if the initial data of pseudo Calabi flow has volume form C⁰ close to a smooth one, then the flow is immediately smooth for t>0. As an application, we show that if the initial data has volume form C⁰ close to that of a cscK metric, then the pseudo Calabi flow exists for t∈ (0,+∞). We also prove similar improvement of regularity and long time existence result for pseudo Calabi flow on a Fano manifold when the volume form is bounded and the class is close to c₁(M).Other curvature flowsKähler geometryLong-time existence & convergenceKähler–Einstein & K-stability