相关论文: A geometric interpretation of Hamilton's Harnack i…

We show that in dimension 4 and above, the lifespan of Ricci flows depends on the relative smallness of the Ricci curvature compared to the Riemann curvature on the initial manifold. We can generalize this lifespan estimate to the local…

We prove that if the Ricci curvature is uniformly bounded under the Ricci-Harmonic flow for all times $t$ \in[0, T), then the curvature tensor has to be uniformly bounded as well.

In the present paper, we introduce a concept of Ricci curvature on hypergraphs for a nonlinear Laplacian. We prove that our definition of the Ricci curvature is a generalization of Lin-Lu-Yau coarse Ricci curvature for graphs to…

A theory of gravitation is proposed, modeled after the notion of a Ricci flow. In addition to the metric an independent volume enters as a fundamental geometric structure. Einstein gravity is included as a limiting case. Despite being a…

The aim of this short note is to produce new examples of geometrical flows associated to a given Riemannian flow $g(t)$. The considered flow in covariant symmetric $2$-tensor fields will be called Ricci-Yamabe map since it involves a scalar…

Motivated by a question of Tsai-Tsui-Wang, we consider the rigidity of map from manifolds with positive Ricci curvature to manifolds with positive sectional curvature. We show that if the Ricci curvature of the domain dominates that of the…

We investigate the K\"ahler-Ricci flow modified by a holomorphic vector field. We find equivalent analytic criteria for the convergence of the flow to a K\"ahler-Ricci soliton. In addition, we relate the asymptotic behavior of the scalar…

It is the purpose of this article to establish a technical tool to study regularity of solutions to parabolic equations on manifolds. As applications of this technique, we prove that solutions to the Ricci-DeTurck flow, the surface…

In this paper, we establish a framework for the analysis of linear parabolic equations on conical surfaces and use them to study the conical Ricci flow. In particular, we prove the long time existence of the conical Ricci flow for general…

The famous Uniformization Theorem states that on closed Riemannian surfaces there always exists a metric of constant curvature for the Levi-Cevita connection. In this article we prove that an analogue of the uniformization theorem also…

In this paper, we consider the Laplacian G_2 flow on a closed seven-dimensional manifold M with a closed G_2-structure. We first obtain the gradient estimates of positive solutions of the heat equation under the Laplacian G_2 flow and then…

In this article we get a time-dependent Sobolev inequality along the Ricci flow which generalizes the earlier results of Zhang, Ye, Hsu. As an application of the time-dependent Sobolev inequality, we also get a growth of the ratio of…

In this note, we want to establish several formulas about functionals along harmonic Ricci flow on surface with boundary

We present a family of topological quantum gravity theories associated with the geometric theory of the Ricci flow on Riemannian manifolds. First we use BRST quantization to construct a "primitive" topological Lifshitz-type theory for only…

This paper studies the normalized Ricci flow from a slight perturbation of the hyperbolic metric on $\mathbb H^n$. It's proved that if the perturbation is small and decays sufficiently fast at the infinity, then the flow will converge…

We simplify and improve the curvature estimates in the paper: On the conditions to extend Ricci flow(II). Furthermore, we develop some volume estimates for the Ricci flow with bounded scalar curvature. These estimates can be applied to…

We develop different synthetic notions of Ricci flow in the setting of time-dependent metric measure spaces based on ideas from optimal transport. They are formulated in terms of dynamic convexity and local concavity of the entropy along…

In this paper, we introduce a new combinatorial curvature on triangulated surfaces with inversive distance circle packing metrics. Then we prove that this combinatorial curvature has global rigidity. To study the Yamabe problem of the new…

If g(t) is a three-dimensional Ricci flow solution, with sectional curvatures that decay like the inverse of t and diameter that increases at most like the square root of t, then the pullback Ricci flow solution on the universal cover…

We show the existence of a solution to the Ricci flow with a compact length space of bounded curvature, i.e., a space that has curvature bounded above and below in the sense of Alexandrov, as its initial condition. We show that this flow…