General mixed width-integral of convex bodies

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August undefined, 2024

WebAbstract. In this article, we introduce a new concept of general mixed width-integral of convex bodies, and establish some of its inequalities, such as isoperimetric inequality, Aleksandrov-Fenchel inequality, and cyclic inequality. We also consider the general width-integral of order i and show its related properties and inequalities. WebThe mixed width-integrals are defined and shown to have properties similar to those of the mixed volumes of Minkowski. An inequality is established for the mixed width-integrals …

General Lp-mixed width-integral of convex bodies and related ...

WebSep 1, 2010 · The mixed width-integrals of convex bodies are defined by E. Lutwak. In this paper, the mixed brightness-integrals of convex bodies are defined. An inequality is established for the mixed brightness-integrals analogous to the Fenchel-Aleksandrov inequality for the mixed volumes. An isoperimetric inequality (involving the mixed … WebSep 26, 2024 · Further, two cyclic inequalities for the differences of i-th general Lp-mixed width-integral of convex bodies are obtained. Discover the world's research 20+ million members fabian michalski

Dual Brunn–Minkowski inequality for volume differences

WebApr 10, 2024 · In 2016, Feng gave the definitions of mixed width-integral and the general i-th width-integral of convex bodies. In 2024, Zhou defined the general L p-mixed width-integral of convex bodies. For the more results of the mixed width-integral of convex bodies, we refer the interested reader to Refs. [7-14]. WebNov 14, 2024 · Recently, the general width-integral of index i was introduced and some of its isoperimetric inequalities were established. In this paper, we establish some new … fabian miller tallahassee

New Brunn-Minkowski Type Inequalities for General …

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WebApr 10, 2024 · In 1975 Lutwak introduced the i-th width-integral of convex bodies. In 1977, Lutwak generalized the i-th width-integral to the mixed width-integral of convex bodies. In … WebFeb 12, 2016 · The notion of general mixed chord integrals of star bodies was introduced by Feng and Wang. In this paper, we extend the concept of the general mixed chord integrals to general $L_{p}$-mixed chord integrals of star bodies.Based on this new notion, we study their extremum values and obtain an Aleksandrov-Frenchel type and a … fabian michlerWebNow let us discuss the case of a general semigroup of integral points. Let SˆZn be a semigroup. Let Gbe the subgroup of Zn generated by S, Lthe subspace of Rnspanned by Sand Cthe closure of the convex hull of S[f0g, that is, the smallest closed convex cone (with apex at the origin) containing S. Clearly, Gand Care contained in the subspace L. does hyundai make a third row suv

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General mixed width-integral of convex bodies

$General $L_{p}$ -mixed chord integrals of star bodies - Springer$

WebA general result for a convex body K and a convex increasing real valued function gives inequalities for sets of constant width and sets with equichordal points as special cases. Preliminaries By a convex body in Rn , n > 2, we mean a compact convex subset of Rn with nonempty interior. All convex bodies are assumed to contain the origin WebSep 25, 2024 · A complex convex body is uniquely determined by its support function , where “∙” means the standard Hermitian inner production in and is the real part of . ... Some Inequalities about the General Lp-Mixed Width-Integral of Convex Bodies Wuhan University Journal of Natural Sciences, 2024, Vol. 27 No.4, 281-286.

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WebAbstract: General mixed width-integral of convex bodies is introduced. We prove some important inequalities, such as, isoperimetric inequali-ty, Aleksandrov-Fenchel inequality … WebIn this article, we introduce a new concept of general mixed width-integral of convex bodies, and establish some of its inequalities, such as isoperimetric inequality, …

WebJun 15, 2016 · In this article, we introduce a new concept of general mixed width-integral of convex bodies, and establish some of its inequalities, such as isoperimetric … WebSep 22, 2009 · Lutwak E.: Mixed width-integrals of convex bodies. Israel J. Math. 28(3), 249–253 (1977) ... Mercer, A.M.: Extensions of Popoviciu’s inequality using a general method. J. Ineq. Pure Appl. Math. 4 Article 11, 4 pp (2003) Google Scholar Schneider R.: Convex Bodies: The Brunn–Minkowski Theory. Cambridge University Press, New York …

WebJul 1, 1994 · General integral geometric invariants for convex bodies are introduced and two integral geometric inequalities for them are established. ... Boundary structure 3. Minkowski addition 4. Curvature measure and quermass integrals 5. Mixed volumes 6. ... we obtain some results about the mean curvature integrals of the outer parallel convex … WebAs an application, inequalities are given between the projection measures of convex bodies and the mixed projection integrals of the bodies. References. A. D. Aleksandrov, Extension of certain concepts in the theory of convex bodies, Mat. …

WebJul 15, 2024 · Lutwak, E.: Mixed width-integrals of convex bodies. Isr. J. Math. 28(3), 249–253 (1977) Article MathSciNet MATH Google Scholar Feng, Y.B.: General mixed …

Web1500 YIBIN FENG AND WEIDONG WANG Lutwak [23] introduced the notion of mixed width-integrals of convex bodies. Motivated by Lutwak’s ideas, the notion of mixed chord-integrals of fabian michael paderbornWebJun 15, 2016 · General mixed width-integral of convex bodies. In this article, we introduce a new concept of general mixed width-integral of convex bodies, and establish some … does hyundai have start stop technologyWebJan 27, 2024 · Keywords: general width-integral; volume difference type inequality; Blaschke-Minkowski homomorphism; Brunn-Minkowski type inequality; projection body Classification MSC: 52A20, 52A40 DOI: 10.21136/CMJ.2024.0521-18 fabian michelsonWebApr 10, 2024 · The Brunn-Minkowski type and the cyclic Brunn-Minkowski type inequalities for the i-th general L p-mixed width-integral of convex bodies are established. … does hyundai make a sports carWebdeﬁnition of mixed chord-integrals to the general mixed chord-integrals of star bodies: For M 1;:::;M n 2 S o n and ˝ 2 (1; 1), the general mixed chord-integral, ... is the group of rotations in n dimensions. M+ ~ N denotes the radial Minkowski addition of M ... continuous and rigid motion invariant valuations on convex bodies. The book (see ... does hyundai offer 0 percent financingWebNov 30, 2024 · The mean width for a log-concave function is introduced by Klartag, Milman and Rotem (see [22, ... is a natural extension of the mixed Quermassintegrals of convex bodies in \ ... and the invariance of the integral by translation of coordinates, we know that holds with equality. On the ... fabian michaelWebSep 10, 2024 · In this article, we introduce the concept of general Lp-mixed chord integral difference of star bodies. Further, we establish the Brunn–Minkowski type, Aleksandrov–Fenchel type and cyclic inequalities for the Lp-mixed chord integral difference. ... Lutwak, E. Mixed width-integrals of convex bodies. Israel J. Math. … fabian michael and jane