On the evolution by fractional mean curvature

Mariel Saez, Enrico Valdinoci

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)


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
Issue number1
Publication statusPublished - 2019


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