https://neckpinch.com/authors/yu-zeng/New arXiv papers by Yu Zeng, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1701.06943/arxiv:1701.06943Tue, 24 Jan 2017 00:00:00 GMTWeiyong He, Yu Zeng — In this paper, we prove that there exists a dimensional constant δ> 0 such that given any background Kähler metric ω, the Calabi flow with initial data u₀ satisfying \beginequation* \partial \bar \partial u_0 \in L^\infty (M) and (1- δ)ω< ω_u_0 < (1+δ)ω, \endequation* admits a unique short time solution and it becomes smooth immediately, where ω_(u₀) : = ω+√(−1)∂bar∂u₀. The existence time depends on initial data u₀ and the metric ω. As a corollary, we get that Calabi flow has short time existence for any initial data satisfying \beginequation* \partial \bar \partial u_0 \in C^0(M) and ω_u_0 > 0, \endequation* which should be interpreted as a "continuous Kähler metric". A main technical ingredient is Schauder-type estimates for biharmonic heat equation on Riemannian manifolds with time weighted Hölder norms.Other curvature flowsKähler geometryWeak & singular flowsHarmonic maps & DeTurck trickKähler–Einstein & K-stability