Affine isoperimetric problems
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 ... WebClick on the article title to read more.
Affine isoperimetric problems
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WebJan 15, 2024 · In the present paper, we prove existence and continuity of the extremal general affine surface areas (1)and (2). Our main result is a Blaschke-Santaló type inequality for the inner maximal Lφaffine surface area. 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...
WebNov 7, 2024 · Over the last two decades several important affine isoperimetric inequalities, comparing geometric functionals which are invariant under volume preserving affine or … 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 …
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 … 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 …
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 … christchurch angling club dorsetWebWe give a stability version of of the Blaschke-Santaló inequality in the plane. christ church anglican southern pines ncWebOct 1, 2024 · A set of new sharp affine isoperimetric inequalities for these volume decomposition functionals in R3 are established, which essentially characterize the geometric and algebraic structures of... geometry postulates examplesWebAug 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. geometry powerpoint lessonsWebPetty, C. M.: Affine Isoperimetric problems in: Discrete Geometry and Convexity (eds J. E. Goodman, E. Lutwak, J. Malkevitch and R. Pollack); Ann. New York Acad. Sci. 440 (1985), 113–127. Google Scholar Reisz, F.: Sur une inegalite integrale, J. London Math. Soc. 5 (1930), 162–168. Google Scholar Rogers, C. A. and Shephard, G. C.: geometry postulates listWebJan 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]. geometry postulate sheetWebThe book then tackles geometric algorithms, convexity and discrete optimization, mathematical programming and convex geometry, and the combinatorial aspects … geometry postulates pdf