TY - JOUR
T1 - Type II singularities in area-preserving curvature flows of convex symmetric immersed closed plane curves
AU - Anada, Koichi
AU - Ishiwata, Tetsuya
AU - Ushijima, Takeo
N1 - Publisher Copyright:
© 2025 The Author(s)
PY - 2025/8/25
Y1 - 2025/8/25
N2 - We deal with the area-preserving curvature flow in the plane, particularly the blow-up phenomena of curvatures on cusp singularities in contractions of convex immersed curves with self-crossing points. For Abresch-Langer type curves with highly symmetric properties, it has been known that the maximum of curvatures blows up at a finite time under some assumptions. In this paper, we consider the blow-up rates in this case.
AB - We deal with the area-preserving curvature flow in the plane, particularly the blow-up phenomena of curvatures on cusp singularities in contractions of convex immersed curves with self-crossing points. For Abresch-Langer type curves with highly symmetric properties, it has been known that the maximum of curvatures blows up at a finite time under some assumptions. In this paper, we consider the blow-up rates in this case.
KW - Area-preserving flows
KW - Blow-up phenomena
KW - Curvature flows
KW - Immersed plane curves
KW - Type II singularities
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U2 - 10.1016/j.jde.2025.113348
DO - 10.1016/j.jde.2025.113348
M3 - Article
AN - SCOPUS:105003247767
SN - 0022-0396
VL - 437
JO - Journal of Differential Equations
JF - Journal of Differential Equations
M1 - 113348
ER -