Curve shortening flow on Riemann surfaces with possible ambient conic singularities

DOI10.1016/j.difgeo.2022.101895zbMath1496.53105arXiv2007.00089OpenAlexW3039008950WikidataQ114190875 ScholiaQ114190875MaRDI QIDQ2672328

Biao Ma

Publication date: 8 June 2022

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.00089

zbMATH Keywords

conic singularitiesGage-Hamilton-Grayson theoremHuisken's comparison function

Mathematics Subject Classification ID

Riemann surfaces (30F99) Geometric evolution equations (53E99)

Cites Work

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• Ricci flow on surfaces with conical singularities
• On the formation of singularities in the curve shortening flow
• Asymptotic behavior for singularities of the mean curvature flow
• The normalized curve shortening flow and homothetic solutions
• The heat equation shrinking convex plane curves
• The heat equation shrinks embedded plane curves to round points
• Singularities of the curve shrinking flow for space curves
• Monotonicity formulas for parabolic flows on manifolds
• Shortening embedded curves
• A distance comparison principle for evolving curves
• On the structure of spaces with Ricci curvature bounded below. I
• Polar coordinates on singular Riemannian surfaces
• Harnack estimate for the mean curvature flow
• Two-point functions and their applications in geometry
• Curvature bound for curve shortening flow via distance comparison and a direct proof of Grayson's theorem
• Curve shortening on surfaces
• The isoperimetric inequality

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