Explanipedia

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Open

Aijin Lin, Li Wu · 2025

Ge in his thesis \cite{Ge-thesis} introduced the combinatorial Calabi flows and established the long time existence and convergence of solutions to the flows in both hyperbolic and Euclidean background geometries. It is noteworthy that the…

Branched $α$-combinatorial Ricci flows on closed surfaces with Euler characteristic $χ\leq 0$ Open

Wei Li, Rongyuan Liu, Guanrong Chen, Aijin Lin · 2025

This paper investigates branched $α$-flows on branched weighted triangulated closed surfaces with Euler characteristic $χ\leq 0$, focusing on establishing their connections with topological-combinatorial structures and geometric structur…

The Kähler–Ricci flow on pseudoconvex domains Open

Huabin Ge, Aijin Lin, Liangming Shen · 2019

We establish the existence of the Kähler-Ricci flow on pseudoconvex domains with general initial metrics without curvature bounds.We could show that the evolving metric is simultaneously complete, and the corresponding normalized Kähler-Ri…

Positive solutions of p-th Yamabe type equations on graphs Open

Xiaoxiao Zhang, Aijin Lin · 2018

Combinatorial $p$-th Calabi flows on surfaces Open

Aijin Lin, Xiaoxiao Zhang · 2018

For triangulated surfaces and any $p>1$, we introduce the combinatorial $p$-th Calabi flow which precisely equals the combinatorial Calabi flows first introduced in H. Ge's thesis when $p=2$. The difficulties for the generalizations come f…

Positive solutions of $p$-th Yamabe type equations on infinite graphs Open

Xiaoxiao Zhang, Aijin Lin · 2018

Let $G=(V,E)$ be a connected infinite and locally finite weighted graph, and let $\Delta _p$ be the $p$-th discrete graph Laplacian. In this paper, we consider the $p$-th Yamabe type equation \begin{equation*} -\Delta _pu+h|u|^{p-2}u=gu^{\…

The Kähler-Ricci flow on pseudoconvex domains Open

Huabin Ge, Aijin Lin, Liangming Shen · 2018

We establish the existence of Kähler-Ricci flow on pseudoconvex domains with general initial metric without curvature bounds. Moreover we prove that this flow is simultaneously complete, and its normalized version converge to the complete …

Gradient flow of the norm squared of a moment map over Kahler manifolds Open

Aijin Lin, Liangming Shen · 2018

Inspired by Wilkin's work [23, 24] on Morse theory for the moduli space of Higgs bundles, we study the moduli space of gauged holomorphic maps by a heat flow approach in the spirit of Atiyah and Bott in a series of papers. In this paper, a…

Mean Curvature Type Flows of Graphs in Product Manifolds Open

Aijin Lin, Hengyu Zhou · 2017

In this note we study a large class of mean curvature type flows of graphs in product manifold $N\times R$ where N is a closed Riemann- ian manifold. Their speeds are the mean curvature of graphs plus a prescribed function. We establish lo…

Conic Kähler-Einstein metrics along simple normal crossing divisors on Fano manifolds Open

Aijin Lin, Liangming Shen · 2016

We prove that on one Kähler-Einstein Fano manifold without holomorphic vector fields, there exists a unique conical Kähler-Einstein metric along a simple normal crossing divisor with admissible prescribed cone angles. We also establish a c…

Conic K\"{a}hler-Einstein metrics along simple normal crossing divisors on Fano manifolds Open

Aijin Lin, Liangming Shen · 2016

We prove that on one K\"{a}hler-Einstein Fano manifold without holomorphic vector fields, there exists a unique conical K\"{a}hler-Einstein metric along a simple normal crossing divisor with admissible prescribed cone angles. We also estab…

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