Type II ancient compact solutions to the Yamabe flow

DOI10.1515/crelle-2015-0048zbMath1472.53102arXiv1209.5479OpenAlexW2963085897MaRDI QIDQ1747184

Natasa Sesum, Panagiota Daskalopoulos, Manuel A. del Pino

Publication date: 4 May 2018

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.5479

zbMATH Keywords

perturbationcontracting spheresancient compact solutionsfirst-order Toda systemKing solutionstower of two spheres

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Conformal structures on manifolds (53C18) Ricci flows (53E20)

Related Items (29)

Ancient gradient flows of elliptic functionals and Morse index ⋮ Bubble towers in the ancient solution of energy-critical heat equation ⋮ Bubbling and extinction for some fast diffusion equations in bounded domains ⋮ Yamabe solitons with boundary ⋮ Collapsing and noncollapsing in convex ancient mean curvature flow ⋮ Infinite-time blowing-up solutions to small perturbations of the Yamabe flow ⋮ Extinction behavior for the fast diffusion equations with critical exponent and Dirichlet boundary conditions ⋮ Singularity formation in the harmonic map flow with free boundary ⋮ The Cauchy-Dirichlet problem for the fast diffusion equation on bounded domains ⋮ Fine properties of solutions to the Cauchy problem for a fast diffusion equation with Caffarelli-Kohn-Nirenberg weights ⋮ Solutions with single radial interface of the generalized Cahn-Hilliard flow ⋮ Geometry driven type II higher dimensional blow-up for the critical heat equation ⋮ Ancient Solutions in Geometric Flows ⋮ Asymptotic behaviour of singular solution of the fast diffusion equation in the punctured Euclidean space ⋮ Finite time blow-up for the fractional critical heat equation in \(\mathbb{R}^n\) ⋮ Construction of two-bubble solutions for some energy-critical wave equations ⋮ Asymptotic large time behavior of singular solutions of the fast diffusion equation ⋮ Infinite time blow-up for critical heat equation with drift terms ⋮ Singularity formation for the two-dimensional harmonic map flow into \(S^2\) ⋮ Infinite-time blow-up for the 3-dimensional energy-critical heat equation ⋮ Type II finite time blow-up for the energy critical heat equation in \(\mathbb{R}^4\) ⋮ Type II blow-up in the 5-dimensional energy critical heat equation ⋮ Long-time asymptotics for evolutionary crystal dislocation models ⋮ Infinite time blow-up for the fractional heat equation with critical exponent ⋮ Infinite-time incompleteness of noncompact Yamabe flow ⋮ Sign-changing blowing-up solutions for the critical nonlinear heat equation ⋮ Fast diffusion on noncompact manifolds: Well-posedness theory and connections with semilinear elliptic equations ⋮ Ancient mean curvature flows out of polytopes ⋮ Existence of Neumann and singular solutions of the fast diffusion equation

Cites Work

• Classification of ancient compact solutions to the Ricci flow on surfaces
• Compact constant mean curvature surfaces in Euclidean three-space
• Convergence of the Yamabe flow for arbitrary initial energy
• Complete constant mean curvature surfaces in Euclidean three-space
• Global existence and convergence of Yamabe flow
• ``Bubble-tower radial solutions in the slightly supercritical Brezis-Nirenberg problem.
• Bubble towers for supercritical semilinear elliptic equations
• Constant mean curvature surfaces constructed by fusing Wente tori
• Connected sum constructions for constant scalar curvature metrics
• Exact polynomial solutions to some nonlinear diffusion equations
• Convergence of the Yamabe flow in dimension 6 and higher
• Connected sums of constant mean curvature surfaces in Euclidean 3 space
• On the extinction profile for solutions of $u_t=\Delta u^{(N-2)/(N+2)}
• The existence of weak solutions with prescribed singular behavior for a conformally invariant scalar equation
• The yamabe flow on locally conformally flat manifolds with positive ricci curvature
• Convergence of the Yamabe flow for large energies
• Asymptotic results for nonlinear outdiffusion

This page was built for publication: Type II ancient compact solutions to the Yamabe flow