Related papers: One Dimensional Conformal Metric Flows

This paper surveys some selected topics in the theory of conformal metrics and their connections to complex analysis, partial differential equations and conformal differential geometry.

This paper is a review on recently found connection between geodesically equivalent metrics and integrable geodesic flows. Suppose two different metrics on one manifold have the same geodesics. We show that then the geodesic flows of these…

Conformal Ricci and conformal matter collineations for the combination of two perfect fluids in General Relativity are investigated. We study the existence of timelike and spacelike conformal Ricci and matter collineations by introducing…

In this paper, we use less topological restrictions and more geometric and analytic conditions to obtain some sufficient conditions on Yamabe solitons such that their metrics are Yamabe metrics, that is, metrics of constant scalar…

We introduce a new class of discrete conformal structures on surfaces with boundary, which have nice interpolations in 3-dimensional hyperbolic geometry. Then we prove the global rigidity of the new discrete conformal structures using…

This paper aims at building a unified framework to deal with a wide class of local and nonlocal translation-invariant geometric flows. First, we introduce a class of generalized curvatures, and prove the existence and uniqueness for the…

We consider a thermodynamically consistent diffuse interface model describing two-phase flows of incompressible fluids in a non-isothermal setting. This model was recently introduced in a previous paper of ours, where we proved existence of…

In this work, we study the Yamabe flow corresponding to the prescribed scalar curvature problem on compact Riemannian manifolds with negative scalar curvature. The long time existence and convergence of the flow are proved under appropriate…

We study the problem of deforming a Riemannian metric to a conformal one with nonzero constant scalar curvature and nonzero constant boundary mean curvature on a compact manifold of dimension $n\geq 3$. We prove the existence of such…

Let (M,g) be a compact Riemannian manifold with boundary. This paper addresses the Yamabe-type problem of finding a conformal scalar-flat metric on M, which has the boundary as a constant mean curvature hypersurface. When the boundary is…

Carlotto, Chodosh and Rubinstein have studied the convergence rate of the Yamabe flow. Inspired by their result, we study the convergence rate of the $Q$-curvature flow in this paper. In particular, we provide an example of a slowly…

We classify certain sofic shifts (the irreducible Point Extension Type, or PET, sofic shifts) up to flow equivalence, using invariants of the canonical Fischer cover. There are two main ingredients: (1) An extension theorem, for extending…

We define a formal Riemannian metric on a given conformal class of metrics on a closed Riemann surface. We show interesting formal properties for this metric, in particular the curvature is nonpositive and the Liouville energy is…

This paper is devoted to the study of weak and strong convergence of derivations, and of the flows associated to them, when dealing with a sequence of metric measure structures (X,d,m_n), m_n weakly convergent to m. In particular, under…

We describe a family of generalized almost structures associated with a Monge-Amp\`ere equation for a stream function of 2D incompressible fluid flows. Using an indefinite metric field constructed from a pair of $2$-forms related to the…

One dimensional metrical geometry may be developed in either an affine or projective setting over a general field using only algebraic ideas and quadratic forms. Some basic results of universal geometry are already present in this…

We construct new ancient compact solutions to the Yamabe flow. Our solutions are rotationally symmetric and converge, as $t \to -\infty$, to two self-similar complete non-compact solutions to the Yamabe flow moving in opposite directions.…

Using the conformally invariant Cotton tensor, we define a geometric flow, the "Cotton flow", which is exclusive to three dimensions. This flow tends to evolve the initial metrics into conformally flat ones, and is somewhat orthogonal to…

We study the Yamabe flow on a Riemannian manifold of dimension $m\geq3$ minus a closed submanifold of dimension $n$ and prove that there exists an instantaneously complete solution if and only if $n>\frac{m-2}{2}$. In the remaining cases…

The metric flow is introduced and extensively studied by Bamler [Bam20b, Bam20c], especially as an $\mathbb{F}$-limit of a sequence of smooth Ricci flows with uniformly bounded Nash entropy, in which case each regular point on the limit is…