On the Isoperimetric Inequality and Surface Diffusion Flow for Multiply Winding Curves
Keyword(s):
Abstract In this paper we establish a general form of the isoperimetric inequality for immersed closed curves (possibly non-convex) in the plane under rotational symmetry. As an application, we obtain a global existence result for the surface diffusion flow, providing that an initial curve is $$H^2$$ H 2 -close to a multiply covered circle and is sufficiently rotationally symmetric.
2019 ◽
Vol 113
(1)
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pp. 1-53
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1998 ◽
pp. 69-80
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2020 ◽
Vol 237
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pp. 1325-1382
2002 ◽
Vol 2
(3)
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pp. 349-364
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2013 ◽
Vol 45
(5)
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pp. 2834-2869
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1998 ◽
Vol 29
(6)
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pp. 1419-1433
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2021 ◽
Vol 29
(5)
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pp. 1007-1060