A sharp Rogers and Shephard inequality for the $p$-difference body of planar convex bodies

Chiara Bianchini, Andrea Colesanti

Type: Article

Publication Date: 2008-03-10

Citations: 17

DOI: https://doi.org/10.1090/s0002-9939-08-09209-5

Abstract

We prove a sharp Rogers and Shephard type inequality for the $p$-difference body of a convex body in the two-dimensional case, for every $p\ge 1$.

Locations

Proceedings of the American Mathematical Society - View - PDF

Similar Works

Action	Title	Year	Authors
+	A sharp Rogers-Shephard type inequality for the p-difference body of a planar convex body	2007	Chiara Bianchini Andrea Colesanti
+	A sharp Rogers–Shephard type inequality for Orlicz-difference body of planar convex bodies	2014	Hailin Jin Shufeng Yuan
+	Rogers and Shephard inequality for the Orlicz difference body	2015	Fangwei Chen Wenxue Xu Congli Yang
+	The role of the Rogers–Shephard inequality in the characterization of the difference body	2016	Judit Abardia-Evéquoz Eugenia Saorín Gómez
+ PDF Chat	Inequalities for the Difference Body of a Convex Body	1967	G. D. Chakerian
+ PDF Chat	On unbalanced difference bodies and Godbersen's conjecture	2024	Shiri Artstein-Avidan Eli Putterman
+	The difference body of a convex body	1957	C. A. Rogers G. C. Shephard
+ PDF Chat	A REVERSE ISOPERIMETRIC INEQUALITY FOR PLANAR (α, β)−CONVEX BODIES	2021	Gisella Croce Zakaria Fattah Giovanni Pisante
+ PDF Chat	A sharp isoperimetric bound for convex bodies	2006	Ravi Montenegro
+	The role of the Rogers-Shephard inequality in the characterization of the difference body	2016	Judit Abardia Eugenia Saorín Gómez
+	The role of the Rogers-Shephard inequality in the characterization of the difference body	2016	Judit Abardia Eugenia Saorín Gómez
+ PDF Chat	Asymmetric $L_p$-difference bodies	2014	Weidong Wang Tongyi Ma
+	Banach–Mazur distance of planar convex bodies	2007	Marek Lassak
+	Stone-Weierstrass theorem for homogeneous polynomials and its role in convex geometry	2020	Bernardo González Merino Rafael Villa
+	Extremal Banach-Mazur distance between a symmetric convex body and an arbitrary convex body on the plane	2017	Tomasz Kobos
+	Extremal Banach-Mazur distance between a symmetric convex body and an arbitrary convex body on the plane	2017	Tomasz Kobos
+	Stone-Weierstrass theorem for homogeneous polynomials and its role in convex geometry	2020	Bernardo González Merino Rafael Villa
+	Sections of the difference body	1998	Mark Rudelson
+	Distances between non--symmetric convex bodies and the $MM^*$-estimate	1998	Mark Rudelson
+	On Reverses of the Blaschke-Santalo Inequality for Convex Bodies	2013	Wang Weidong Weidong Zhou Yanping

Works That Cite This (17)

Action	Title	Year	Authors
+	On Rogers-Shephard type inequalities for the lattice point enumerator	2021	David Alonso–Gutiérrez Eduardo Lucas Jesús Yepes Nicolás
+	The Orlicz centroid inequality for star bodies	2011	Guangxian Zhu
+	The Brunn–Minkowski–Firey inequality for nonconvex sets	2011	Erwin Lutwak Deane Yang Gaoyong Zhang
+	Orlicz projection bodies	2009	Erwin Lutwak Deane Yang Gaoyong Zhang
+ PDF Chat	On successive radii of p-sums of convex bodies	2014	Bernardo González Merino María A. Hernández Cifre
+	On Brunn–Minkowski Type Inequalities and Overdetermined Problem for p-Capacity	2020	Lewen Ji
+ PDF Chat	On Rogers–Shephard-type inequalities for the lattice point enumerator	2022	David Alonso‐Gutiérrez Eduardo Lucas Jesús Yepes Nicolás
+	The Orlicz Brunn–Minkowski inequality	2014	Dongmeng Xi Hailin Jin Gangsong Leng
+	Symmetrizations	2023	Gabriele Bianchi Paolo Gronchi
+	Some Inequalities in Convex Geometry	2013	Steven Taschuk

Works Cited by This (18)

Action	Title	Year	Authors
+ PDF Chat	On volume product inequalities for convex sets	2006	Stefano Campi Paolo Gronchi
+ PDF Chat	On the $L_{p}$-Minkowski problem	2003	Erwin Lutwak Deane Yang Gaoyong Zhang
+ PDF Chat	Sharp Affine LP Sobolev Inequalities	2002	Erwin Lutwak Deane Yang Gaoyong Zhang
+ PDF Chat	The Brunn-Minkowski-Firey theory. I. Mixed volumes and the Minkowski problem	1993	Erwin Lutwak
+	Convex Bodies: The Brunn–Minkowski Theory	1993	Rolf Schneider
+	Extremum Problems with Inequalities as Subsidiary Conditions	2013	Fritz John
+	On the reverse <i> L <sup>p</sup> </i> –busemann–petty centroid inequality	2002	Stefano Campi Paolo Gronchi
+	Some extremal problems for convex bodies	1958	C. A. Rogers G. C. Shephard
+	The difference body of a convex body	1957	C. A. Rogers G. C. Shephard
+	Shadow systems of convex sets	1964	G. C. Shephard