Related papers: Yamabe Flow: steady solitons and type II singulari…
This work concerns with the existence and detailed asymptotic analysis of Type II singularities for solutions to complete non-compact conformally flat Yamabe flow with cylindrical behavior at infinity. We provide the specific blow-up rate…
In this paper we classify rotationally symmetric conformally flat admissible solitons to the $k$-Yamabe flow, a fully non-linear version of the Yamabe flow. For $n\geq 2k$ we prove existence of complete expanding, steady and shrinking…
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.…
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.…
This work addresses the {\em singularity formation} of complete non-compact solutions to the conformally flat Yamabe flow whose conformal factors have {\em cylindrical behavior at infinity}. Their singularity profiles happen to be {\em…
We show that an eternal solution to a complete, locally conformally flat Yamabe flow, $\frac{\partial}{\partial t} g = -Rg$, with uniformly bounded scalar curvature and positive Ricci curvature at $t = 0$, where the scalar curvature assumes…
In this work, we study the convergence of the normalized Yamabe flow with positive Yamabe constant on a class of pseudo-manifolds that includes stratified spaces with iterated cone-edge metrics. We establish convergence under a low energy…
We construct new type II ancient compact solutions to the Yamabe flow. Our solutions are rotationally symmetric and converge, as $t \to -\infty$, to a tower of two spheres. Their curvature operator changes sign. We allow two time-dependent…
In this paper we investigate the structure of certain solutions of the fully nonlinear Yamabe flow, which we call quotient almost Yamabe solitons because they extend quite naturally those called quotient Yamabe solitons. We then present…
We show the noninheritance of the completeness of the noncompact Yamabe flow. Our main theorem states the existence of a long time solution which is complete for each time and converges to an incomplete Riemannian metric. This shows the…
In this work we establish long-time existence of the normalized Yamabe flow with positive Yamabe constant on a class of manifolds that includes spaces with incomplete cone-edge singularities. We formulate our results axiomatically, so that…
We provide the classification of locally conformally flat gradient Yamabe solitons with positive sectional curvature. We first show that locally conformally flat gradient Yamabe solitons with positive sectional curvature have to be…
We review recent compactness and non-compactness results for the Yamabe equation. We also discuss the asymptotic behavior of the parabolic Yamabe flow.
We give a survey of various compactness and non-compactness results for the Yamabe equation. We also discuss a conjecture of Hamilton concerning the asymptotic behavior of the parabolic Yamabe flow.
In this work we introduce a family of conformal flows generalizing the classical Yamabe flow. We prove that for a large class of such flows long-time existence holds, and the arguments are in fact simpler than in the classical case.…
This article is concerned with developing an analytic theory for second order nonlinear parabolic equations on singular manifolds. Existence and uniqueness of solutions in an Lp-framework is established by maximal regularity tools. These…
Under the validity of the positive mass theorem, the Yamabe flow on a smooth compact Riemannian manifold of dimension $N \ge 3$ is known to exist for all time $t$ and converges to a solution to the Yamabe problem as $t \to \infty$. We prove…
In this paper, we study the combinatorial Yamabe flow on infinite triangulated surfaces in Euclidean background geometry, aiming for solving discrete Yamabe problem on noncompact surfaces. Under suitable conditions, we establish the…
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…
This article presents an analysis of the normalized Yamabe flow starting at and preserving a class of compact Riemannian manifolds with incomplete edge singularities and negative Yamabe invariant. Our main results include uniqueness,…