### Abstract

In particular, we give examples of neckpinch singularity formation, and we discuss convexity properties of the evolution.

We also take into account traveling waves for this geometric flow, showing that a new family of C 1 , 1 and convex traveling sets arises in this setting.

Original language | English |
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Pages (from-to) | 1-21 |

Journal | Journal of the London Mathematical Society |

DOIs | |

Publication status | E-pub ahead of print - 20 Jul 2018 |

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**On a Minkowski geometric flow in the plane: Evolution of curves with lack of scale invariance.** / Dipierro, S.; Novaga, M.; Valdinoci, E.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On a Minkowski geometric flow in the plane: Evolution of curves with lack of scale invariance

AU - Dipierro, S.

AU - Novaga, M.

AU - Valdinoci, E.

PY - 2018/7/20

Y1 - 2018/7/20

N2 - We consider a planar geometric flow in which the normal velocity is a nonlocal variant of the curvature. The flow is not scaling invariant and in fact has different behaviors at different spatial scales, thus producing phenomena that are different with respect to both the classical mean curvature flow and the fractional mean curvature flow.In particular, we give examples of neckpinch singularity formation, and we discuss convexity properties of the evolution.We also take into account traveling waves for this geometric flow, showing that a new family of C 1 , 1 and convex traveling sets arises in this setting.

AB - We consider a planar geometric flow in which the normal velocity is a nonlocal variant of the curvature. The flow is not scaling invariant and in fact has different behaviors at different spatial scales, thus producing phenomena that are different with respect to both the classical mean curvature flow and the fractional mean curvature flow.In particular, we give examples of neckpinch singularity formation, and we discuss convexity properties of the evolution.We also take into account traveling waves for this geometric flow, showing that a new family of C 1 , 1 and convex traveling sets arises in this setting.

U2 - 10.1112/jlms.12162

DO - 10.1112/jlms.12162

M3 - Article

SP - 1

EP - 21

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

SN - 0024-6107

ER -