TY - JOUR
T1 - On the Isoperimetric Inequality and Surface Diffusion Flow for Multiply Winding Curves
AU - Miura, Tatsuya
AU - Okabe, Shinya
N1 - Funding Information:
Tatsuya Miura was supported by JSPS KAKENHI Grant Numbers 18H03670 and 20K14341, and by Grant for Basic Science Research Projects from The Sumitomo Foundation. Shinya Okabe was supported by JSPS KAKENHI Grant Numbers 19H05599 and 16H03946. Part of this work was done while the authors were visiting the Institute for Mathematics and its Applications, University of Wollongong. The authors acknowledge the hospitality and are grateful to Professor Glen Wheeler for his kind invitation and encouragement.
Funding Information:
Tatsuya Miura was supported by JSPS KAKENHI Grant Numbers 18H03670 and 20K14341, and by Grant for Basic Science Research Projects from The Sumitomo Foundation. Shinya Okabe was supported by JSPS KAKENHI Grant Numbers 19H05599 and 16H03946. Part of this work was done while the authors were visiting the Institute for Mathematics and its Applications, University of Wollongong. The authors acknowledge the hospitality and are grateful to Professor Glen Wheeler for his kind invitation and encouragement.
Publisher Copyright:
© 2020, The Author(s).
PY - 2021/2
Y1 - 2021/2
N2 - 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 H2-close to a multiply covered circle and is sufficiently rotationally symmetric.
AB - 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 H2-close to a multiply covered circle and is sufficiently rotationally symmetric.
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U2 - 10.1007/s00205-020-01591-7
DO - 10.1007/s00205-020-01591-7
M3 - Article
AN - SCOPUS:85095769227
VL - 239
SP - 1111
EP - 1129
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
SN - 0003-9527
IS - 2
ER -