Lp-dual geominimal surface areas for the general Lp-intersection bodies
نویسندگان
چکیده
For 0 < p < 1, Haberl and Ludwig defined the notions of symmetric and asymmetric Lp-intersection bodies. Recently, Wang and Li introduced the general Lp-intersection bodies. In this paper, we give the Lp-dual geominimal surface area forms for the extremum values and Brunn-Minkowski type inequality of general Lp-intersection bodies. Further, combining with the Lp-dual geominimal surface areas, we consider Busemann-Petty type problem for general Lp-intersection bodies. c ©2017 All rights reserved.
منابع مشابه
Lp-Dual geominimal surface area
* Correspondence: [email protected] Department of Mathematics, China Three Gorges University, Yichang, 443002, China, Abstract Lutwak proposed the notion of Lp-geominimal surface area according to the Lpmixed volume. In this article, associated with the Lp-dual mixed volume, we introduce the Lp-dual geominimal surface area and prove some inequalities for this notion. 2000 Mathematics Subject Cla...
متن کاملLp-Minkowski and Aleksandrov-Fenchel type inequalities
In this paper we establish the Lp-Minkowski inequality and Lp-Aleksandrov-Fenchel type inequality for Lp-dual mixed volumes of star duality of mixed intersection bodies, respectively. As applications, we get some related results. The paper new contributions that illustrate this duality of projection and intersection bodies will be presented. M.S.C. 2000: 52A40.
متن کاملThe mixed L p - dual affine surface area for multiple star bodies
Associated with the notion of the mixed Lp-affine surface area for multiple convex bodies for all real p (p 6= −n) which was introduced by Ye, et al. [D. Ye, B. Zhu, J. Zhou, arXiv, 2013 (2013), 38 pages], we define the concept of the mixed Lp-dual affine surface area for multiple star bodies for all real p (p 6= −n) and establish its monotonicity inequalities and cyclic inequalities. Besides, ...
متن کاملA Characterization of Lp Intersection Bodies
All GL(n) covariant Lp radial valuations on convex polytopes are classified for every p > 0. It is shown that for 0 < p < 1 there is a unique non-trivial such valuation with centrally symmetric images. This establishes a characterization of Lp intersection bodies. 2000 AMS subject classification: 52A20 (52B11, 52B45)
متن کاملINTERSECTION BODIES AND Lp-SPACES
In this talk we discuss a new connection between convex geometry and the theory of Lp-spaces. It appears that intersection bodies, one the main objects of convex geometry, are directly related to the concept of embedding of normed spaces in Lp with p < 0. This allows to get new geometric results by extending different facts about Lp-spaces to negative values of p. We present several application...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017