Displaying similar documents to “Free boundary minimal surfaces: a survey of recent results”

The asymptotic behaviour of surfaces with prescribed mean curvature near meeting points of fixed and free boundaries

Frank Müller (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We study the shape of stationary surfaces with prescribed mean curvature in the Euclidean 3-space near boundary points where Plateau boundaries meet free boundaries. In deriving asymptotic expansions at such points, we generalize known results about minimal surfaces due to G. Dziuk. The main difficulties arise from the fact that, contrary to minimal surfaces, surfaces with prescribed mean curvature do not meet the support manifold perpendicularly along their free boundary, in general. ...

Alessio Figalli's contributionsto nonlocal minimal surfaces

Serena Dipierro, Enrico Valdinoci (2019)

Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana

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Alessio has produced in his very intense career an extraordinary number of outstanding results in an impressive variety of topics. Among the multifold research lines in which he acted as a trailblazer, the one focused on nonlocal minimal surfaces offered an excellent opportunity for Alessio to pioneer some of the first settlements in a brand new subject of investigation and pave the way to a broad spectrum of future research.