A monotonicity formula for minimal sets with a sliding boundary condition
David, Guy (Université Paris-Sud)

Data: 2016
Resum: We prove a monotonicity formula for minimal or almost minimal sets for the Hausdorff measure Hd, subject to a sliding boundary constraint where competitors for E are obtained by deforming E by a one-parameter family of functions yt such that yt(x) ∈ L when x ∈ E lies on the boundary L. In the simple case when L is an affine subspace of dimension d-1, the monotone or almost monotone functional is given by F(r) = r-d Hd (E∩B(x, r)) + r-d Hd (S∩B(x,r)) where x is any point of E (not necessarily on L) and S is the shade of L with a light at x. We then use this, the description of the case when F is constant, and a limiting argument, to give a rough description of E near L in two simple cases.
Drets: Tots els drets reservats
Llengua: Anglès
Document: article ; recerca ; publishedVersion
Matèria: Minimal sets ; Almost minimal sets ; Monotonicity formula ; Sliding boundary condition ; Plateau problem
Publicat a: Publicacions matemàtiques, Vol. 60 Núm. 2 (2016) , p. 335-450 (Articles) , ISSN 2014-4350

Adreça original: http://www.raco.cat/index.php/PublicacionsMatematiques/article/view/10.5565-PUBLMAT_60216_04
DOI: 10.5565/PUBLMAT_60216_04
DOI: 10.5565/10.5565-PUBLMAT_60216_04

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