Results 51 to 60 of about 4,011 (135)
Uniqueness of Solutions to a Nonlinear Elliptic Hessian Equation
Journal of Applied Mathematics, 2016 Through an Alexandrov-Fenchel inequality, we establish the general Brunn-Minkowski inequality. Then we obtain the uniqueness of solutions to a nonlinear elliptic Hessian equation on Sn.
Siyuan Li
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Functional Brunn-Minkowski inequalities induced by polarity
Advances in Mathematics, 2020 We prove a new family of inequalities, which compare the integral of a geometric convolution of non-negative functions with the integrals of the original functions. For classical inf-convolution, this type of inequality is called the Pr kopa-Leindler inequality, which, restricted to indicators of convex bodies, gives the classical Brunn-Minkowski ...
Artstein-Avidan, S. +2 more
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Functional Geominimal Surface Area and Its Related Affine Isoperimetric Inequality
Journal of Function Spaces, Volume 2020, Issue 1, 2020., 2020 The first variation of the total mass of log‐concave functions was studied by Colesanti and Fragalà, which includes the Lp mixed volume of convex bodies. Using Colesanti and Fragalà’s first variation formula, we define the geominimal surface area for log‐concave functions, and its related affine isoperimetric inequality is also established.
Niufa Fang, Jin Yang, Chang-Jian Zhao
wiley +1 more source
Some new Brunn-Minkowski-type inequalities in convex bodies
International Journal of Mathematics and Mathematical Sciences, 2005 We establish some analogues of the Brunn-Minkowski inequalities on convex bodies and the Minkowski inequality and their inverse versions. As an application, we generalize and improve some interrelated results.
Zhao Chang-Jian +2 more
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On the Discrete Orlicz Electrostatic q‐Capacitary Minkowski Problem
Journal of Function Spaces, Volume 2020, Issue 1, 2020., 2020 We establish the existence of solutions to the Orlicz electrostatic q‐capacitary Minkowski problem for polytopes. This contains a new result of the discrete Lp electrostatic q‐capacitary Minkowski problem for p < 0and 1 < q < n.
Yibin Feng, Yanping Zhou, Youjiang Lin
wiley +1 more source
More on logarithmic sums of convex bodies [PDF]
, 2014 We prove that the log-Brunn-Minkowski inequality (log-BMI) for the Lebesque measure in dimension $n$ would imply the log-BMI and, therefore, the B-conjecture for any log-concave density in dimension $n$.
Saroglou, Christos
core +1 more source
Fractional generalizations of Young and Brunn-Minkowski inequalities
, 2011 A generalization of Young's inequality for convolution with sharp constant is conjectured for scenarios where more than two functions are being convolved, and it is proven for certain parameter ranges.
Bobkov, Sergey +2 more
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Dual Orlicz geominimal surface area
Journal of Inequalities and Applications, 2016 The L p $L_{p}$ -geominimal surface area was introduced by Lutwak in 1996, which extended the important concept of the geominimal surface area. Recently, Wang and Qi defined the p-dual geominimal surface area, which belongs to the dual Brunn-Minkowski ...
Tongyi Ma, Weidong Wang
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The dimensional Brunn–Minkowski inequality in Gauss space
Journal of Functional Analysis, 2021 Let $ _n$ be the standard Gaussian measure on $\mathbb{R}^n$. We prove that for every symmetric convex sets $K,L$ in $\mathbb{R}^n$ and every $ \in(0,1)$, $$ _n( K+(1- )L)^{\frac{1}{n}} \geq _n(K)^{\frac{1}{n}}+(1- ) _n(L)^{\frac{1}{n}},$$ thus settling a problem raised by Gardner and Zvavitch (2010).
Eskenazis, Alexandros +1 more
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The Dual Log-Brunn-Minkowski Inequalities [PDF]
Taiwanese Journal of Mathematics, 2016 In this article, we establish the dual log-Brunn-Minkowski inequality and the dual log-Minkowski inequality. Moreover, the equivalence between the dual log-Brunn-Minkowski inequality and the dual log-Minkowski inequality is demonstrated.
Wang, Wei, Liu, Lijuan
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