Related papers: Chern-Simons classes and the Ricci flow on 3-manif…

In this paper we study the Ricci flow on surfaces homeomorphic to a cylinder (that is, a product of the circle with a compact interval). We prove longtime existence results, results on the asymptotic behavior of the flow, and we report on…

U(1) Chern-Simons theory is quantized canonically on manifolds of the form $M=\mathbb{R}\times\Sigma$, where $\Sigma$ is a closed orientable surface. In particular, we investigate the role of mapping class group of $\Sigma$ in the process…

In this short note, we observe that the Bamler-Kleiner proof of uniqueness and stability for 3-dimensional Ricci flow through singularities generalizes to singular Ricci flows in higher dimensions that satisfy an analogous canonical…

In this note, we extend the theory of Chern-Cheeger-Simons to construct canonical invariants for a one-parameter family of flat connections on a smooth manifold. These invariants lie in degrees $(2p-2)$-cohomology with $\C/\Z$-cohomology,…

In \cite{ChauMartens} the authors proved the long-time existence of Ricci flow starting from complete bounded curvature Riemannian manifolds with scale-invariant integral curvature bounded by a dimensional constant times the inverse of the…

We prove that the Ricci flow g(t) starting at any metric on the euclidean space that is invariant by a transitive nilpotent Lie group N, can be obtained by solving an ODE for a curve of nilpotent Lie brackets. By using that this ODE is the…

This paper studies the normalized Ricci flow on surfaces with conical singularities. It's proved that the normalized Ricci flow has a solution for a short time for initial metrics with conical singularities. Moreover, the solution makes…

[Dedicated to Richard S. Hamilton on forty years of Ricci flow] Gradient Ricci solitons have garnered significant attention both as self-similar solutions and singularity models of the Ricci flow. This survey article starts with a list of…

We prove the short-time existence of Ricci flows on complete manifolds with scalar curvature bounded below uniformly, Ricci curvature bounded below by a negative quadratic function, and with almost Euclidean isoperimetric inequality holds…

We construct the classical mechanics associated with a conformally flat Riemannian metric on a compact, n-dimensional manifold without boundary. The corresponding gradient Ricci flow equation turns out to equal the time-dependent…

In this work, we are going to find sufficient conditions on the initial triaxial Bianchi IX metric on some 4-dimensional manifolds foliated by homogeneous S3 for a Type I singularity to occur when it is flowed under the Ricci flow. This…

The purpose of this article is to study an $f$-cosymplectic manifold $M$ admitting Ricci solitons. Here we consider mainly two classes of Ricci solitons on $f$-cosymplectic manifolds. One is the class of contact Ricci solitons. The other is…

We explore the harmonic-Ricci flow---that is, Ricci flow coupled with harmonic map flow---both as it arises naturally in certain principal bundle constructions related to Ricci flow and as a geometric flow in its own right. We demonstrate…

A new approach to the quantization of Chern-Simons theory has been developed in recent papers of the author. It uses a "simulation" of the moduli space of flat connections modulo the gauge group which reveals to be related to a lattice…

In this paper, we study the behavior of Ricci flows on compact orbifolds with finite singularities. We show that Perelman's pseudolocality theorem also holds on orbifold Ricci flow. Using this property, we obtain a weak compactness theorem…

In this work, we use the Ricci flow approach to study the gap phenomenon of Riemannian manifolds with non-negative curvature and sub-critical scaling invariant curvature decay. The first main result is a quantitative Ricci flow existence…

In this paper, we prove a pseudolocality-type theorem for $\mathcal L$-complete noncompact Ricci flow which may not have bounded sectional curvature; with the help of it we study the uniqueness of the Ricci flow on noncompact manifolds. In…

We show that an orientable 3-dimensional manifold M admits a complete riemannian metric of bounded geometry and uniformly pos- itive scalar curvature if and only if there exists a finite collection F of spherical space-forms such that M is…

In this article, we shall investigate the relationship between the existence or non-existence of non-singular solutions to the normalized Ricci flow and smooth structures on closed 4-manifolds, where non-singular solutions to the normalized…

In this paper, we establish the existence and uniqueness of Ricci flow that admits an embedded closed convex surface in $\mathbb{R}^3$ as metric initial condition. The main point is a family of smooth Ricci flows starting from smooth convex…