Affine isoperimetric problems

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August undefined, 2024

WebApr 10, 2009 · In this new affine analytic inequality an affine energy of the gradient replaces the standard L n energy of gradient. The geometric inequality at the core of the affine Moser–Trudinger inequality is a recently established affine isoperimetric inequality for … WebWe give a stability version of of the Blaschke-Santaló inequality in the plane.

Lp Geominimal Surface Areas and their Inequalities

WebAug 6, 2010 · New L p isocapacitary and isoperimetric inequalities are proved for Lipschitz star bodies. It is shown that the sharp convex Lorentz–Sobolev inequalities are analytic analogues of isocapacitary and isoperimetric inequalities. Download to read the full article text References Adams D.R.: A sharp inequality of J. Moser for higher order derivatives. WebNov 7, 2024 · Over the last two decades several important affine isoperimetric inequalities, comparing geometric functionals which are invariant under volume preserving affine or … equality diversity inclusion discrimination

Handbook of Convex Geometry ScienceDirect

WebJan 1, 1993 · As a result many very important sharp affine isoperimetric inequalities are not even mentioned. For example, it would be difficult to name an affine inequality more beautiful than the Rogers-Shephard (1957, 1958) difference body inequality [and its extensions by Chakerian (1967), Schneider (1970), and others]. WebFeb 1, 2024 · In this paper, we consider the optimization problems associated with the nonhomogeneous and homogeneous Orlicz mixed torsional rigidities by investigating the properties of the corresponding... WebJun 5, 2012 · THE LOGARITHMIC MINKOWSKI PROBLEM KÁROLY J. BÖRÖCZKY, ERWIN LUTWAK, DEANE YANG, AND GAOYONG ZHANG 1. ... studied in [41], [42], and [35]. Applications of the Lp-surface area measure to affine isoperimetric inequalities were given in, e.g., [6], [40], and [45]. THE LOGARITHMIC MINKOWSKI PROBLEM 833 The … finding profitable products to sell on amazon

New Lp affine isoperimetric inequalities - ScienceDirect

Isoperimetric problems - ResearchGate

WebSep 10, 2024 · Unlike the classical isoperimetric inequalities, the affine isoperimetric inequalities are inequalities between a pair of geometric functionals whose product is invariant under affine... WebMar 1, 2024 · Our Theorem 1.1is proved by using the Steiner symmetrization, which is a well-known powerful tool for the isoperimetric problem as well as its affine analogue. For the sets of finite perimeter, Chlebík-Cianchi-Fusco [5]characterized the equality cases of the Steiner's inequalityS(E)≥S(SuE). equality diversity unit oxford universityWebAffine isoperimetric inequalities related to the L p geominimal surface area were proved for p=1 in [30, 31] and for p>1 in . Roughly speaking, those affine isoperimetric inequalities assert that among all convex bodies with fixed volume and with centroid at the origin (the condition on the centroid can be removed for p =1), the L p geominimal ... finding programs windows 10

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Affine isoperimetric problems

Sharp convex Lorentz–Sobolev inequalities SpringerLink

Web(13) Wang Weidong（王卫东） and Leng Gangsong， Some affine isoperimetric inequalities associated with Lp-affine surface area, Houston Journal of Mathematics, 2008, 34(2): 443-453. ... (25) Wang Weidong（王卫东） and Wan Xiaoyan，Shephard type problems for general Lp-projection bodies，Taiwanese Journal of … WebDec 16, 2006 · The polar projection inequality of Petty [44], providing the classical relation between the volume of a convex body and its polar projection body, is an affine invariant …

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WebWe call such problems isoperimetric type problems. It is a very natural question to ask if such isoperimetric type problems also hold in the hyperbolic space Hn. We remark that in this paper Hn denotes the hyperbolic space with the sectional curvature −1. One of main motivations to study this problem comes naturally from integral geometry in ... WebJun 20, 2008 · Introduction An affine isoperimetric inequality relates two functionals associated with convex bodies (or more general sets) where the ratio of the functionals is …

WebMar 26, 2024 · The Blaschke–Santaló inequality was proven by W. Blaschke in 1917, for $ n = 2,3 $, and by L. Santaló in 1949, for all $ n \geq 2 $. Both proofs use the affine isoperimetric inequality of affine differential geometry and the solution of the Minkowski problem. The fact that only ellipsoids attain the upper bound in the Blaschke–Santaló ... WebApr 21, 2024 · The isoperimetric problem, which dates back to the ancient Greeks, is to determine among all planar gures with xed perimeter the one with the largest area. The …

WebOct 25, 2024 · Concerning ellipsoids associated with projection functions and their applications in the solution of affine isoperimetric problems, we refer to . 2 Preliminaries … WebDec 1, 1992 · PDF On Dec 1, 1992, A. Martínez and others published Affine isoperimetric problems and surfaces with constant affine mean curvature Find, read and cite all the …

WebMay 15, 2024 · In this article, several sharp affine isoperimetric inequalities for U1(K, L) are established. Theorem 1.1. If P, Q are convex polytopes in Rn and Q is origin-symmetric, then V(ΠP)V(Q) U1(P, Q)n 2V1(P, Q)n 2 ≤ 2n(nn n!)1 2, (1.8) with equality if and only if P and Q are parallel parallelotopes. Theorem 1.2.

WebOct 1, 2016 · An affine isoperimetric inequality in the Orlicz–Brunn–Minkowski theory provides upper and/or lower bounds, in terms of volume, for functionals defined on … finding promo codes in source codeWebThe Isoperimetric Problem Viktor Bl asj˚ o¨ 1. ANTIQUITY. To tell the story of the isoperimetric problem one must begin by quoting Virgil: At last they landed, where from far your eyes May view the turrets of new Carthage rise; There bought a space of ground, which Byrsa call’d, From the bull’s hide they ﬁrst inclos’d, and wall’d. equality diversity \u0026 human rights week 2022WebMar 24, 2024 · Isoperimetric Problem. Find a closed plane curve of a given perimeter which encloses the greatest area. The solution is a circle . If the class of curves to be … equality diversity unit oxfordWebL p affine isoperimetric inequalities 113 mechanics. However, the L p-analogues of projection bodies are new.In order to correctly deﬁne them one needs the recently introduced (in [21] [22]) notion of L p-curvature.Both the L p-analogues of centroid bodies and the L p-analogues of projection bodies belong to the class Zn p of L p- zonoids. finding promotional credits on amazonWebApr 30, 2024 · Affine vs. Euclidean isoperimetric inequalities Christoph Haberl, Franz E. Schuster It is shown that every even, zonal measure on the Euclidean unit sphere gives rise to an isoperimetric inequality for sets … equality diversity lawsWebisoperimetric problem, in mathematics, the determination of the shape of the closed plane curve having a given length and enclosing the maximum area. (In the absence of any … equality doctrineWebA purely analytic proof is given for an inequality that has as a direct consequence the two most important affine isoperimetric inequalities of plane convex geometry: The … finding property investors uk