2024 Affine isoperimetric problems

Affine isoperimetric problems

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August undefined, 2024

WebA 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 … Web1 day ago · The Lp (where 1≤p≤∞) centroid bodies with respect to weights that are powers of the distance to the origin (i.e., x ℓ with ℓ>−n) and their associated…

Isoperimetric problems - ResearchGate

WebL 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. 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 ... rudys offroad adventures youtube

The isoperimetric problem - University of Washington

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 … 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). rudys nutrition info

Lp Geominimal Surface Areas and their Inequalities

Functional Geominimal Surface Area and Its Related Affine Isoperimetric ...

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 18, 2024 · Affine fractional isoperimetric inequalities are established that are stronger (and directly imply) the Euclidean fractional isoperimetric inequalities. ... of solutions of weighted isoperimetric-type problems … rudys music new york cityWebApr 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 … rudys norman menu

"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 … " - Affine isoperimetric problems

Affine isoperimetric problems

Affine isoperimetric inequalities in the functional Orlicz–Brunn ...

WebThe book then tackles geometric algorithms, convexity and discrete optimization, mathematical programming and convex geometry, and the combinatorial aspects … WebOct 25, 2024 · Concerning ellipsoids associated with projection functions and their applications in the solution of affine isoperimetric problems, we refer to . 2 Preliminaries …

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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 … WebThe 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.

WebSep 7, 2024 · The classical Blaschke-Santaló inequality is one of the essential affine isoperimetric inequalities in convex geometric analysis (see, e.g., [13], [57]), which states that if K is an origin-symmetric convex body in R n, then (4.1) V (K) V (K ⁎) ≤ ω n 2, with equality if and only if K is an origin-centered ellipsoid. 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.

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]. WebThroughout this paper, a convex body is defined as a compact convex set with interior points in Euclidean n-dimensional space En. The oldest of these problems is called the a f h e …

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 …

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... rudys northwest freewayWebClick on the article title to read more. scaramouche themeWebDec 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 … rudys of apex ncWebJun 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 … scaramouche theme lyricsWebSep 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... scaramouche the balladeerWebWe give a stability version of of the Blaschke-Santaló inequality in the plane. scaramouche theme midiWebMay 15, 2024 · A new affine invariant geometric functional for convex polytopes is introduced. Some new sharp affine isoperimetric inequalities are established for this … scaramouche theme phase 2