Ancient Solutions in Geometric Flows

DOI10.1007/978-3-030-34953-0_17zbMath1444.53003OpenAlexW2336549947MaRDI QIDQ3300611

Natasa Sesum

Publication date: 29 July 2020

Published in: Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-34953-0_17

zbMATH Keywords

mean curvature flowRicci flowancient solutions

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to differential geometry (53-02) Ricci flows (53E20) Flows related to mean curvature (53E10)

Cites Work

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• Ancient solutions of the mean curvature flow
• Noncollapsing in mean-convex mean curvature flow
• Convex solutions to the mean curvature flow
• Eternal solutions to the Ricci flow
• Classification of ancient compact solutions to the Ricci flow on surfaces
• Flow by mean curvature of convex surfaces into spheres
• On the existence of translating solutions of mean curvature flow in slab regions
• The Ricci flow on the 2-sphere
• Convergence of the Yamabe flow for arbitrary initial energy
• Classification of compact ancient solutions to the curve shortening flow
• Unique asymptotics of ancient convex mean curvature flow solutions
• Type II ancient compact solutions to the Yamabe flow
• Harnack estimate for the mean curvature flow
• Formal asymptotic expansions for symmetric ancient ovals in mean curvature flow
• Exact polynomial solutions to some nonlinear diffusion equations
• Type II ancient solutions to the Ricci flow on surfaces
• Uniqueness of convex ancient solutions to mean curvature flow in \({\mathbb {R}}^3\)
• Graphical translators for mean curvature flow
• Rotational symmetry of self-similar solutions to the Ricci flow
• Convergence of the Yamabe flow in dimension 6 and higher
• Rotational symmetry of Ricci solitons in higher dimensions
• Uniqueness of the bowl soliton
• Mean Curvature Flow of Mean Convex Hypersurfaces
• Self-shrinkers with a rotational symmetry
• Eternal solutions to the Ricci flow on R2
• Refined asymptotics for the blowup of u_t — δu = u^p
• Convergence of the Yamabe flow for large energies
• Curve Lengthening Equation and Its Solutions
• The nature of singularities in mean curvature flow of mean-convex sets
• The size of the singular set in mean curvature flow of mean-convex sets

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