Results 1 to 10 of about 187 (48)
Isoperimetric and Brunn-Minkowski inequalities for the (p, q)-mixed geominimal surface areas
Open Mathematics, 2022 Motivated by the celebrated work of Lutwak, Yang and Zhang [1] on (p,q)\left(p,q)-mixed volumes and that of Feng and He [2] on (p,q)\left(p,q)-mixed geominimal surface areas, we in the present paper establish and confirm the affine isoperimetric and ...
Zhang Juan, Wang Weidong, Zhao Peibiao
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Some inequalities for star duality of the radial Blaschke-Minkowski homomorphisms
Open Mathematics, 2020 In 2006, Schuster introduced the radial Blaschke-Minkowski homomorphisms. In this article, associating with the star duality of star bodies and dual quermassintegrals, we establish Brunn-Minkowski inequalities and monotonic inequality for the radial ...
Zhao Xia, Wang Weidong, Lin Youjiang
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A bound for the perimeter of inner parallel bodies [PDF]
, 2016 We provide a sharp lower bound for the perimeter of the inner parallel sets of a convex body Ω. The bound depends only on the perimeter and inradius r of the original body and states that |∂Ω_t| ≥ (1−t/r)^(n−1)₊|∂Ω|.
Larson, Simon
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Mixed Ehrhart polynomials [PDF]
, 2017 For lattice polytopes $P_1,\ldots, P_k \subseteq \mathbb{R}^d$, Bihan (2014) introduced the discrete mixed volume $\mathrm{DMV}(P_1,\dots,P_k)$ in analogy to the classical mixed volume.
Haase, Christian +3 more
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Bezout Inequality for Mixed volumes [PDF]
, 2016 In this paper we consider the following analog of Bezout inequality for mixed volumes: $$V(P_1,\dots,P_r,\Delta^{n-r})V_n(\Delta)^{r-1}\leq \prod_{i=1}^r V(P_i,\Delta^{n-1})\ \text{ for }2\leq r\leq n.$$ We show that the above inequality is true when ...
Soprunov, Ivan, Zvavitch, Artem
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Open Mathematics, 2018 In this paper, by the Orlicz-Minkowski combinations of convex bodies, we define the general Orlicz difference bodies and study their properties. Furthermore, we obtain the extreme values of the general Orlicz difference bodies and their polars.
Shi Wei, Wang Weidong, Ma Tongyi
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Characterization of Simplices via the Bezout Inequality for Mixed volumes [PDF]
, 2015 We consider the following Bezout inequality for mixed volumes: $$V(K_1,\dots,K_r,\Delta[{n-r}])V_n(\Delta)^{r-1}\leq \prod_{i=1}^r V(K_i,\Delta[{n-1}])\ \text{ for }2\leq r\leq n.$$ It was shown previously that the inequality is true for any $n ...
Saroglou, Christos +2 more
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Minkowski measurability results for self-similar tilings and fractals with monophase generators [PDF]
, 2012 In a previous paper [arXiv:1006.3807], the authors obtained tube formulas for certain fractals under rather general conditions. Based on these formulas, we give here a characterization of Minkowski measurability of a certain class of self-similar tilings
Lapidus, Michel L. +2 more
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Quantitative anisotropic isoperimetric and Brunn-Minkowski inequalities for convex sets with improved defect estimates [PDF]
, 2018 In this paper we revisit the anisotropic isoperimetric and the Brunn-Minkowski inequalities for convex sets. The best known constant $C(n)=Cn^{7}$ depending on the space dimension $n$ in both inequalities is due to Segal [\ref{bib:Seg.}]. We improve that
Harutyunyan, Davit
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A Remark on the Anisotropic Outer Minkowski content [PDF]
, 2012 We study an anisotropic version of the outer Minkowski content of a closed set in Rn. In particular, we show that it exists on the same class of sets for which the classical outer Minkowski content coincides with the Hausdorff measure, and we give its ...
Chambolle, Antonin +2 more
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