Related papers: Spectrum of kinematic fast dynamo operator in Ricc…
We apply an equivariant version of Perelman's Ricci flow with surgery to study smooth actions by finite groups on closed 3-manifolds. Our main result is that such actions on elliptic and hyperbolic 3-manifolds are conjugate to isometric…
Motivated by the long-time behavior of Ricci flows that collapse with bounded curvature, we study expanding Ricci solitons with nilpotent symmetry on vector bundles over a closed manifold. We prove that, under mild assumptions that are…
We introduce the notions of `super-Ricci flows' and `Ricci flows' for time-dependent families of metric measure spaces $(X,d_t,m_t)_{t\in I}$. The former property is proven to be stable under suitable space-time versions of mGH-convergence.…
We introduce the discrete Einstein metrics as critical points of discrete energy on triangulated 3-manifolds, and study them by discrete curvature flow of second (fourth) order. We also study the convergence of the discrete curvature flow.…
In this paper, we adopt combinatorial Ricci curvature flow methods to study the existence of cusped hyperbolic structure on 3-manifolds with torus boundary. For general pseudo 3-manifolds, we prove the long-time existence and the uniqueness…
In this paper we construct solutions to Ricci DeTurck flow in four dimensions on closed manifolds which are instantaneously smooth but whose initial values $g$ are (possibly) non-smooth Riemannian metrics whose components in smooth…
This note is a study of nonnegativity conditions on curvature which are preserved by the Ricci flow. We focus on specific kinds of curvature conditions which we call noncoercive, these are the conditions for which nonnegative curvature and…
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…
This paper is devoted to the investigation of the monotonicity of parabolic frequency functional under conformal Ricci flow defined on a closed Riemannian manifold of constant scalar curvature and dimension not less than 3. Parabolic…
Ricci flow is a natural gradient flow of the Einstein-Hilbert action. Here we consider the analog for the Einstein-Maxwell action, which gives Ricci flow with a stress tensor contribution coupled to a Yang-Mills flow for the Maxwell field.…
In this work, we obtain some existence results of Chern-Ricci Flows and the corresponding Potential Flows on complex manifolds with possibly incomplete initial data. We discuss the behaviour of the solution as $t\rightarrow 0$. These…
Consider a Riemannian manifold $(M^{m}, g)$ whose volume is the same as the standard sphere $(S^{m}, g_{round})$. If $p>\frac{m}{2}$ and $\int_{M} \left\{ Rc-(m-1)g\right\}_{-}^{p} dv$ is sufficiently small, we show that the normalized…
In his seminal work \cite{Ri96}, Rivin characterized finite ideal polyhedra in three-dimensional hyperbolic space. However, the characterization of infinite ideal polyhedra, as proposed by Rivin, has remained a long-standing open problem.…
In this paper, we investigate the behavior of the normalized Ricci flow on asymptotically hyperbolic manifolds. We show that the normalized Ricci flow exists globally and converges to an Einstein metric when starting from a non-degenerate…
An explicit determination of all local conservation laws of kinematic type on moving domains and moving surfaces is presented for the Euler equations of inviscid compressible fluid flow on curved Riemannian manifolds in n>1 dimensions. All…
We prove the existence and uniqueness of a weighted analogue of the Fefferman-Graham ambient metric for manifolds with density. We then show that this ambient metric forms the natural geometric framework for the singular Ricci flow: given a…
In this paper we present several curvature estimates and convergence results for solutions of the Ricci flow. The curvature estimates depend on smallness of certain local space-time integrals of the norm of the Riemann curvature tensor,…
It is a well-known result of T.\,Kato that given a continuous path of square matrices of a fixed dimension, the eigenvalues of the path can be chosen continuously. In this paper, we give an infinite-dimensional analogue of this result,…
We study the spectral stability of Dirichlet eigenvalues on an embedded annulus whose boundary evolves by curve shortening flow while the ambient surface evolves under the two dimensional Ricci flow using variational formulas, Rellich--type…
The study of dynamo action in astrophysical objects classically involves two timescales: the slow diffusive one and the fast advective one. We investigate the possibility of field amplification on an intermediate timescale associated with…