Unconditional existence of conformally hyperbolic Yamabe flows

DOI10.2140/apde.2020.13.1579zbMath1455.53103arXiv1811.08798OpenAlexW2901948899MaRDI QIDQ2210882

Mario B. Schulz

Publication date: 9 November 2020

Published in: Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.08798

zbMATH Keywords

fast diffusion equationhyperbolic spaceYamabe flowunbounded curvatureinstantaneously complete

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Ricci flows (53E20) Geometric evolution equations (53E99)

Related Items (4)

The Yamabe flow on asymptotically flat manifolds ⋮ The Yamabe flow on asymptotically Euclidean manifolds with nonpositive Yamabe constant ⋮ Incomplete Yamabe flows and removable singularities ⋮ Infinite-time incompleteness of noncompact Yamabe flow

Cites Work

• Ricci flow compactness via pseudolocality, and flows with incomplete initial metrics
• Convergence of the Yamabe flow for arbitrary initial energy
• Gap theorems for locally conformally flat manifolds
• Four-manifolds with positive curvature operator
• Implicit partial differential equations
• Global existence and convergence of Yamabe flow
• Ricci flows with unbounded curvature
• Long-time existence of the edge Yamabe flow
• Instantaneously complete Yamabe flow on hyperbolic space
• Uniqueness of instantaneously complete Ricci flows
• Fast diffusion flow on manifolds of nonpositive curvature
• Convergence of the Yamabe flow in dimension 6 and higher
• Yamabe flow on non-compact manifolds with unbounded initial curvature
• Radial fast diffusion on the hyperbolic space
• Existence of Ricci Flows of Incomplete Surfaces
• The yamabe flow on locally conformally flat manifolds with positive ricci curvature
• Convergence of the Yamabe flow for large energies
• Yamabe flow on manifolds with edges
• Pointwise estimates and quasilinear parabolic equations

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