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Notes on the log-Brunn-Minkowski inequality
Böröczky-Lutwak-Yang-Zhang proved the log-Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane in a way that is stronger...
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A nonabelian Brunn–Minkowski inequality
Henstock and Macbeath asked in 1953 whether the Brunn–Minkowski inequality can be generalized to nonabelian locally compact groups; questions along...
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From the Brunn-Minkowski Inequality to a Class of Generalized Poincaré-Type Inequalities for Torsional Rigidity
In this paper, we establish a class of generalized Poincaré-type inequalities for torsional rigidity on the boundary of a convex body of class
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The Multiple Radial Blaschke–Minkowski Homomorphisms
AbstractIn the paper, our main aim is to generalize the mixed radial Blaschke–Minkowski homomorphisms and Aleksandrov–Fenchel inequality for mixed...
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The anisotropic p-capacity and the anisotropic Minkowski inequality
In this paper, we prove a sharp anisotropic L p Minkowski inequality involving the total L p anisotropic mean curvature and the anisotropic p -capacity...
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The Local Logarithmic Brunn-Minkowski Inequality for Zonoids
The aim of this note is to show that the local form of the logarithmic Brunn-Minkowski conjecture holds for zonoids. The proof uses a variant of the...
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The dual Orlicz Brunn–Minkowski inequality for the intersection body
A generalized dual Brunn–Minkowski inequality for the intersection body is established in the framework of the dual Orlicz Brunn–Minkowski theory....
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A Minkowski Inequality for Horowitz–Myers Geon
We prove a sharp inequality for toroidal hypersurfaces in three- and four-dimensional Horowitz–Myers geon. This extend previous results on Minkowski...
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The Alexandrov–Fenchel inequality
To illustrate the strength of this inequality, we observe that it yields the 1st Minkowski inequality and the 2nd Minkowski inequality as particular...
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A Brunn–Minkowski type inequality for extended symplectic capacities of convex domains and length estimate for a class of billiard trajectories
In this paper, we firstly generalize the Brunn–Minkowski type inequality for Ekeland–Hofer–Zehnder symplectic capacity of bounded convex domains...
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The areas log-Minkowski inequality
In this paper, we first propose and establish an Orlicz log-Minkowski inequality for affine surface areas by introducing new concepts of affine...
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A remark on discrete Brunn–Minkowski type inequalities via transportation of measure
We give an alternative proof for discrete Brunn–Minkowski type inequalities, recently obtained by Halikias, Klartag and the author. This proof also...
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Consequences and Extensions of the Brunn-Minkowski Theorem
In this work we study some extensions and consequences of the fundamental Brunn-Minkowski inequality, using two different approaches: on one hand we...
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Some Log-Minkowski Inequalities for (p, q)-Mixed Volume
The notion of ( p , q )-mixed volume was introduced by Lutwak, Yang and Zhang. In this paper, associated with the ( p , q )-mixed volume, we prove a...
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Volumes of Subset Minkowski Sums and the Lyusternik Region
We begin a systematic study of the region of possible values of the volumes of Minkowski subset sums of a collection of M compact sets in
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On Existence of the Even Lp Gaussian Minkowski Problem for p > n
This paper concerns the even L p Gaussian Minkowski problem in n -dimensional Euclidean space ℝ n . The existence of the solution to the even L p Guassian...
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Wave front sets of Riesz type on Minkowski space
This paper focuses on constructing an O (1, 3)-invariant oscillatory integral on Minkowski space. We then proceed to calculate the wave front set of...
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The Torsion Log-Minkowski Problem
In this paper, we deal with the torsion log-Minkowski problem without symmetry assumptions via an approximation argument.