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The mean curvature of a Lipschitz continuous manifold

Elisabetta Barozzi, Eduardo Gonzalez, Umberto Massari (2003)

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

The paper is devoted to the description of some connections between the mean curvature in a distributional sense and the mean curvature in a variational sense for several classes of non-smooth sets. We prove the existence of the mean curvature measure of E by using a technique introduced in [4] and based on the concept of variational mean curvature. More precisely we prove that, under suitable assumptions, the mean curvature measure of E is the weak limit (in the sense of distributions) of the mean...

Twisted spherical means in annular regions in n and support theorems

Rama Rawat, R.K. Srivastava (2009)

Annales de l’institut Fourier

Let Z ( Ann ( r , R ) ) be the class of all continuous functions f on the annulus Ann ( r , R ) in n with twisted spherical mean f × μ s ( z ) = 0 , whenever z n and s > 0 satisfy the condition that the sphere S s ( z ) Ann ( r , R ) and ball B r ( 0 ) B s ( z ) . In this paper, we give a characterization for functions in Z ( Ann ( r , R ) ) in terms of their spherical harmonic coefficients. We also prove support theorems for the twisted spherical means in n which improve some of the earlier results.

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