The area preserving curve shortening flow with Neumann free boundary conditions

Elena Mäder-Baumdicker

Geometric Flows (2015)

  • Volume: 1, Issue: 1
  • ISSN: 2353-3382

Abstract

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We study the area preserving curve shortening flow with Neumann free boundary conditions outside of a convex domain in the Euclidean plane. Under certain conditions on the initial curve the flow does not develop any singularity, and it subconverges smoothly to an arc of a circle sitting outside of the given fixed domain and enclosing the same area as the initial curve.

How to cite

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Elena Mäder-Baumdicker. "The area preserving curve shortening flow with Neumann free boundary conditions." Geometric Flows 1.1 (2015): null. <http://eudml.org/doc/275859>.

@article{ElenaMäder2015,
abstract = {We study the area preserving curve shortening flow with Neumann free boundary conditions outside of a convex domain in the Euclidean plane. Under certain conditions on the initial curve the flow does not develop any singularity, and it subconverges smoothly to an arc of a circle sitting outside of the given fixed domain and enclosing the same area as the initial curve.},
author = {Elena Mäder-Baumdicker},
journal = {Geometric Flows},
keywords = {Geometric analysis; Curve shortening flow; Free boundary; Neumann boundary condition; Singularities; Volume preserving; monotonicity formulas; gradient estimates; limit curves; blowup point},
language = {eng},
number = {1},
pages = {null},
title = {The area preserving curve shortening flow with Neumann free boundary conditions},
url = {http://eudml.org/doc/275859},
volume = {1},
year = {2015},
}

TY - JOUR
AU - Elena Mäder-Baumdicker
TI - The area preserving curve shortening flow with Neumann free boundary conditions
JO - Geometric Flows
PY - 2015
VL - 1
IS - 1
SP - null
AB - We study the area preserving curve shortening flow with Neumann free boundary conditions outside of a convex domain in the Euclidean plane. Under certain conditions on the initial curve the flow does not develop any singularity, and it subconverges smoothly to an arc of a circle sitting outside of the given fixed domain and enclosing the same area as the initial curve.
LA - eng
KW - Geometric analysis; Curve shortening flow; Free boundary; Neumann boundary condition; Singularities; Volume preserving; monotonicity formulas; gradient estimates; limit curves; blowup point
UR - http://eudml.org/doc/275859
ER -

References

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