On the evolution by fractional mean curvature

Mariel Saez, Enrico Valdinoci

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

In this paper we study smooth solutions to a fractional mean curvature flow equation. We establish a comparison principle and consequences such as uniqueness and finite extinction time for compact solutions. We also establish evolutions equations for fractional geometric objects that in turn yield the preservation of certain quantities, such as the positivity of the fractional mean curvature.

Original languageEnglish
Pages (from-to)211-249
Number of pages39
JournalCommunications in Analysis and Geometry
Volume27
Issue number1
DOIs
Publication statusPublished - 2019

Cite this

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abstract = "In this paper we study smooth solutions to a fractional mean curvature flow equation. We establish a comparison principle and consequences such as uniqueness and finite extinction time for compact solutions. We also establish evolutions equations for fractional geometric objects that in turn yield the preservation of certain quantities, such as the positivity of the fractional mean curvature.",
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On the evolution by fractional mean curvature. / Saez, Mariel; Valdinoci, Enrico.

In: Communications in Analysis and Geometry, Vol. 27, No. 1, 2019, p. 211-249.

Research output: Contribution to journalArticle

TY - JOUR

T1 - On the evolution by fractional mean curvature

AU - Saez, Mariel

AU - Valdinoci, Enrico

PY - 2019

Y1 - 2019

N2 - In this paper we study smooth solutions to a fractional mean curvature flow equation. We establish a comparison principle and consequences such as uniqueness and finite extinction time for compact solutions. We also establish evolutions equations for fractional geometric objects that in turn yield the preservation of certain quantities, such as the positivity of the fractional mean curvature.

AB - In this paper we study smooth solutions to a fractional mean curvature flow equation. We establish a comparison principle and consequences such as uniqueness and finite extinction time for compact solutions. We also establish evolutions equations for fractional geometric objects that in turn yield the preservation of certain quantities, such as the positivity of the fractional mean curvature.

KW - FLOW

KW - HYPERSURFACES

KW - REGULARITY

KW - SURFACES

U2 - 10.4310/CAG.2019.v27.n1.a6

DO - 10.4310/CAG.2019.v27.n1.a6

M3 - Article

VL - 27

SP - 211

EP - 249

JO - Communications in Analysis and Geometry

JF - Communications in Analysis and Geometry

SN - 1019-8385

IS - 1

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