Results 61 to 70 of about 636,012 (237)
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
doaj +1 more source
The log-Minkowski inequality of curvature entropy for non-symmetric convex bodies [PDF]
arXiv, 2022 In an earlier paper \cite{mazeng} the authors introduced the notion of curvature entropy, and proved the plane log-Minkowski inequality of curvature entropy under the symmetry assumption. In this paper we demonstrate the plane log-Minkowski inequality of curvature entropy for general convex bodies.
arxiv
Local spectral estimates and quantitative weak mixing for substitution Z${\mathbb {Z}}$‐actions
Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.Abstract The paper investigates Hölder and log‐Hölder regularity of spectral measures for weakly mixing substitutions and the related question of quantitative weak mixing. It is assumed that the substitution is primitive, aperiodic, and its substitution matrix is irreducible over the rationals.
Alexander I. Bufetov +2 more
wiley +1 more source
Some new refinements of the Young, Hölder, and Minkowski inequalities
Journal of Inequalities and Applications, 2023 We prove and discuss some new refined Hölder inequalities for any p > 1 $p>1$ and also a reversed version for 0 < p < 1 $0 ...
Ludmila Nikolova +2 more
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On $\pmb{p}$-quermassintegral differences function [PDF]
arXiv, 2006 In this paper we establish Minkowski inequality and Brunn--Minkowski inequality for $p$-quermassintegral differences of convex bodies. Further, we give Minkowski inequality and Brunn--Minkowski inequality for quermassintegral differences of mixed projection bodies.
arxiv
Higher order Poincare inequalities and Minkowski-type inequalities [PDF]
arXiv, 2021 We observe some higher order Poincare-type inequalities on a closed manifold, which is inspired by Hurwitz's proof of the Wirtinger's inequality using Fourier theory. We then give some geometric implication of these inequalities by applying them on the sphere.
arxiv
Lattices in function fields and applications
Mathematika, Volume 71, Issue 2, April 2025.Abstract In recent decades, the use of ideas from Minkowski's Geometry of Numbers has gained recognition as a helpful tool in bounding the number of solutions to modular congruences with variables from short intervals. In 1941, Mahler introduced an analogue to the Geometry of Numbers in function fields over finite fields.
Christian Bagshaw, Bryce Kerr
wiley +1 more source
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
doaj +1 more source
Excess Versions of the Minkowski and Hölder Inequalities [PDF]
arXiv, 2018 Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.
arxiv
Counting integral points on symmetric varieties with applications to arithmetic statistics
Proceedings of the London Mathematical Society, Volume 130, Issue 4, April 2025.Abstract In this article, we combine Bhargava's geometry‐of‐numbers methods with the dynamical point‐counting methods of Eskin–McMullen and Benoist–Oh to develop a new technique for counting integral points on symmetric varieties lying within fundamental domains for coregular representations.
Arul Shankar +2 more
wiley +1 more source