An isoperimetric bound for a Sobolev constant
Philip S. Crooke (1978)
Colloquium Mathematicae
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Philip S. Crooke (1978)
Colloquium Mathematicae
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R. Schneider (1995)
Discrete & computational geometry
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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.
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.
Martini, Horst, Mustafaev, Zokhrab (2010)
Journal of Inequalities and Applications [electronic only]
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B. Franchi, S. Gallot, R.L. Wheeden (1994)
Mathematische Annalen
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M. Mateljević, M. Pavlović (1985)
Matematički Vesnik
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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...
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.
Neil S. Trudinger (1997)
Journal für die reine und angewandte Mathematik
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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.
L. E. Payne (1985)
Banach Center Publications
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L. Lovász, R. Kannan, M. Simonovits (1995)
Discrete & computational geometry
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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.
Josip E. Pečarić (1982)
Publications de l'Institut Mathématique
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