Stochastic reverse isoperimetric inequalities in the plane
Sign Up to like & getrecommendations! Published in 2021 at "Geometriae Dedicata"
DOI: 10.1007/s10711-021-00656-5
Abstract: In recent years, it has been shown that some classical inequalities follow from a local stochastic dominance for naturally associated random polytopes. We strengthen planar isoperimetric inequalities by attaching a stochastic model to some classical… read more here.
Keywords: isoperimetric inequalities; stochastic reverse; reverse isoperimetric; reverse ... See more keywords
Affine vs. Euclidean isoperimetric inequalities
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DOI: 10.1016/j.aim.2019.106811
Abstract: It is shown that every even, zonal measure on the Euclidean unit sphere gives rise to an isoperimetric inequality for sets of finite perimeter which directly implies the classical Euclidean isoperimetric inequality. The strongest member… read more here.
Keywords: isoperimetric inequalities; affine euclidean; inequality; euclidean isoperimetric ... See more keywords
Sharp affine isoperimetric inequalities for the volume decomposition functionals of polytopes
Sign Up to like & getrecommendations! Published in 2021 at "Advances in Mathematics"
DOI: 10.1016/j.aim.2021.107902
Abstract: Abstract The nth power of the volume functional V n of polytopes P in R n , according to dimensions of the spaces spanned by any n unit outer normal vectors of P, is decomposed… read more here.
Keywords: isoperimetric inequalities; inequalities volume; volume; affine isoperimetric ... See more keywords