Displaying similar documents to “An isoperimetric problem for tetrahedra.”

Isoperimetric problems for a nonlocal perimeter of Minkowski type

Annalisa Cesaroni, Matteo Novaga (2017)

Geometric Flows

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We show a quantitative version of the isoperimetric inequality for a non local perimeter of Minkowski type. We also apply this result to study isoperimetric problems with repulsive interaction terms, under volume and convexity constraints.We prove existence of minimizers, and we describe their shape as the volume tends to zero or to infinity.

Isoperimetric Regions in Rnwith Density rp

Wyatt Boyer, Bryan Brown, Gregory R. Chambers, Alyssa Loving, Sarah Tammen (2016)

Analysis and Geometry in Metric Spaces

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We show that the unique isoperimetric regions in Rn with density rp for n ≥ 3 and p > 0 are balls with boundary through the origin.

A sharp iteration principle for higher-order Sobolev embeddings

Andrea Cianchi, Luboš Pick, Lenka Slavíková (2014)

Banach Center Publications

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We survey results from the paper [CPS] in which we developed a new sharp iteration method and applied it to show that the optimal Sobolev embeddings of any order can be derived from isoperimetric inequalities. We prove thereby that the well-known link between first-order Sobolev embeddings and isoperimetric inequalities translates to embeddings of any order, a fact that had not been known before. We show a general reduction principle that reduces Sobolev type inequalities of any order...

Direct and Reverse Gagliardo-Nirenberg Inequalities from Logarithmic Sobolev Inequalities

Matteo Bonforte, Gabriele Grillo (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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We investigate the connection between certain logarithmic Sobolev inequalities and generalizations of Gagliardo-Nirenberg inequalities. A similar connection holds between reverse logarithmic Sobolev inequalities and a new class of reverse Gagliardo-Nirenberg inequalities.

Comparison theorems of isoperimetric type for moments of compact sets.

F. G. Avkhadiev, I. R. Kayumov (2004)

Collectanea Mathematica

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A unified approach to prove isoperimetric inequalities for moments and basic inequalities of interpolation spaces L(p,q) is developed. Instead symmetrization methods we use a monotonicity property of special Stiltjes' means.

On unit balls and isoperimetrices in normed spaces

Horst Martini, Zokhrab Mustafaev (2012)

Colloquium Mathematicae

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The purpose of this paper is to continue the investigations on the homothety of unit balls and isoperimetrices in higher-dimensional Minkowski spaces for the Holmes-Thompson measure and the Busemann measure. Moreover, we show a strong relation between affine isoperimetric inequalities and Minkowski geometry by proving some new related inequalities.