Mean curvature of a measure and related variational problems

Guy Bouchitté; Giuseppe Buttazzo; Ilaria Fragalà

Displaying similar documents to “Mean curvature of a measure and related variational problems”

On a functional depending on curvature and edges

Carlo-Romano Grisanti (2001)

Rendiconti del Seminario Matematico della Università di Padova

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Comparison between the generalized mean curvature according to Allard and Federer's mean curvature measure

E. Ossanna (1992)

Rendiconti del Seminario Matematico della Università di Padova

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The mean curvature measure

Quiyi Dai, Neil S. Trudinger, Xu-Jia Wang (2012)

Journal of the European Mathematical Society

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We assign a measure to an upper semicontinuous function which is subharmonic with respect to the mean curvature operator, so that it agrees with the mean curvature of its graph when the function is smooth. We prove that the measure is weakly continuous with respect to almost everywhere convergence. We also establish a sharp Harnack inequality for the minimal surface equation, which is crucial for our proof of the weak continuity. As an application we prove the existence of weak solutions...

A measure theoretic approach to higher codimension mean curvature flows

Luigi Ambrosio, Halil Mete Soner (1997)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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On integral currents with constant mean curvature

Frank Duzaar, Martin Fuch (1991)

Rendiconti del Seminario Matematico della Università di Padova

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Curvature bounds for neighborhoods of self-similar sets

Steffen Winter (2011)

Commentationes Mathematicae Universitatis Carolinae

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In some recent work, fractal curvatures $C_{k}^{f} (F)$ and fractal curvature measures $C_{k}^{f} (F, \cdot)$ , $k = 0, ..., d$ , have been determined for all self-similar sets $F$ in $ℝ^{d}$ , for which the parallel neighborhoods satisfy a certain regularity condition and a certain rather technical curvature bound. The regularity condition is conjectured to be always satisfied, while the curvature bound has recently been shown to fail in some concrete examples. As a step towards a better understanding of its meaning, we discuss several equivalent...

Boundaries of prescribed mean curvature

Eduardo H. A. Gonzales, Umberto Massari, Italo Tamanini (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The existence of a singular curve in $R^{2}$ is proven, whose curvature can be extended to an $L^{2}$ function. The curve is the boundary of a two dimensional set, minimizing the length plus the integral over the set of the extension of the curvature. The existence of such a curve was conjectured by E. De Giorgi, during a conference held in Trento in July 1992.