Richard J. Gardner

Generating author description...

All published works

Action	Title	Year	Authors
+	The Pólya-Szegő inequality for smoothing rearrangements	2024	Gabriele Bianchi Richard J. Gardner Paolo Gronchi Markus Kiderlen
+ PDF Chat	Convergence of symmetrization processes	2022	Gabriele Bianchi Richard J. Gardner Paolo Gronchi
+ PDF Chat	Full rotational symmetry from reflections or rotational symmetries in finitely many subspaces	2022	Gabriele Bianchi Richard J. Gardner Paolo Gronchi
+	The Pólya-Szegő inequality for smoothing rearrangements	2022	Gabriele Bianchi Richard J. Gardner Paolo Gronchi Markus Kiderlen
+	WASHEK PFEFFER November 14, 1936 — January 3, 2021	2021	Richard J. Gardner
+	Rearrangement and polarization	2020	Gabriele Bianchi Richard J. Gardner Paolo Gronchi Markus Kiderlen
+	Rearrangement and polarization	2019	Gabriele Bianchi Richard J. Gardner Paolo Gronchi Markus Kiderlen
+ PDF Chat	General volumes in the Orlicz–Brunn–Minkowski theory and a related Minkowski problem II	2019	Richard J. Gardner Daniel Hug Sudan Xing Deping Ye
+ PDF Chat	General volumes in the Orlicz–Brunn–Minkowski theory and a related Minkowski problem I	2018	Richard J. Gardner Daniel Hug Wolfgang Weil Sudan Xing Deping Ye
+ PDF Chat	Operations between functions	2018	Richard J. Gardner Markus Kiderlen
+	General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski Problem II	2018	Richard J. Gardner Daniel Hug Sudan Xing Deping Ye
+	General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski Problem I	2018	Richard J. Gardner Daniel Hug Wolfgang Weil Sudan Xing Deping Ye
+	Symmetrization in geometry	2016	Gabriele Bianchi Richard J. Gardner Paolo Gronchi
+ PDF Chat	Characterizing the dual mixed volume via additive functionals	2016	Paolo Dulio Richard J. Gardner Carla Peri
+ PDF Chat	Reverse and dual Loomis-Whitney-type inequalities	2015	Stefano Campi Richard J. Gardner Paolo Gronchi
+	The dual Orlicz–Brunn–Minkowski theory	2015	Richard J. Gardner Daniel Hug Wolfgang Weil Deping Ye
+ PDF Chat	The Orlicz-Brunn-Minkowski theory: A general framework, additions, and inequalities	2014	Richard J. Gardner Daniel Hug Wolfgang Weil
+	A characterization of Blaschke addition	2014	Richard J. Gardner Lukas Parapatits Franz E. Schuster
+	Characterizing the dual mixed volume via additive functionals	2013	Paolo Dulio Richard J. Gardner Carla Peri
+	Reverse and dual Loomis-Whitney-type inequalities	2013	Stefano Campi Richard J. Gardner Paolo Gronchi
+ PDF Chat	Operations between sets in geometry	2013	Richard J. Gardner Daniel Hug Wolfgang Weil
+ PDF Chat	Geometric reconstruction methods for electron tomography	2013	Andreas Alpers Richard J. Gardner Stefan König Robert S. Pennington Chris Boothroyd Lothar Houben Rafal E. Dunin‐Borkowski Kees Joost Batenburg
+	THE ORLICZ-BRUNN-MINKOWSKI THEORY: A GENERAL FRAMEWORK, ADDITIONS, AND INEQUALITIES	2013	Richard J. Gardner Daniel Hug Wolfgang Weil
+	The Orlicz-Brunn-Minkowski theory: A general framework, additions, and inequalities	2013	Richard J. Gardner Daniel Hug Wolfgang Weil
+	Reverse and dual Loomis-Whitney-type inequalities	2013	Stefano Campi Richard J. Gardner Paolo Gronchi
+	Characterizing the dual mixed volume via additive functionals	2013	Paolo Dulio Richard J. Gardner Carla Peri
+	Lightness functions	2012	Stefano Campi Richard J. Gardner Paolo Gronchi Markus Kiderlen
+ PDF Chat	Determining a Rotation of a Tetrahedron from a Projection	2012	Richard J. Gardner Paolo Gronchi Thorsten Theobald
+ PDF Chat	A problem of Klee on inner section functions of convex bodies	2012	Richard J. Gardner Dmitry Ryabogin Vlad Yaskin Artem Zvavitch
+	Operations between sets in geometry	2012	Richard J. Gardner Daniel Hug Wolfgang Weil
+	Operations between sets in geometry	2012	Richard J. Gardner Daniel Hug Wolfgang Weil
+	Determining a rotation of a tetrahedron from a projection	2011	Richard J. Gardner Paolo Gronchi Thorsten Theobald
+ PDF Chat	Intersections of dilatates of convex bodies	2011	Stefano Campi Richard J. Gardner Paolo Gronchi
+	A problem of Klee on inner section functions of convex bodies	2011	Richard J. Gardner Dmitri Ryabogin Vladyslav Yaskin Artem Zvavitch
+	Determining a rotation of a tetrahedron from a projection	2011	Richard J. Gardner Paolo Gronchi Thorsten Theobald
+	A problem of Klee on inner section functions of convex bodies	2011	Richard J. Gardner Dmitri Ryabogin Vladyslav Yaskin Artem Zvavitch
+ PDF Chat	Phase retrieval for characteristic functions of convex bodies and reconstruction from covariograms	2010	Gabriele Bianchi Richard J. Gardner Markus Kiderlen
+ PDF Chat	Gaussian Brunn-Minkowski inequalities	2010	Richard J. Gardner Artem Zvavitch
+	Capacities, surface area, and radial sums	2009	Richard J. Gardner David Hartenstine
+	The dual Brunn–Minkowski theory for bounded Borel sets: Dual affine quermassintegrals and inequalities	2007	Richard J. Gardner
+	Parallel X-rays of planar convex bodies	2006	Richard J. Gardner
+	Projections and projection functions	2006	Richard J. Gardner
+	Mixed volumes and dual mixed volumes	2006	Richard J. Gardner
+	Chord functions and equichordal problems	2006	Richard J. Gardner
+	Integral transforms	2006	Richard J. Gardner
+ PDF Chat	Convergence of algorithms for reconstructing convex bodies and directional measures	2006	Richard J. Gardner Markus Kiderlen Peyman Milanfar
+	Shape Estimation from Support and Diameter Functions	2006	Amyn Poonawala Peyman Milanfar Richard J. Gardner
+	Shape discrimination by total curvature, with a view to cancer diagnostics	2005	Richard J. Gardner Asger Hobolth Eva B. Vedel Jensen Flemming Brandt Sørensen
+	Geometric tomography and local stereology	2003	Richard J. Gardner Eva B. Vedel Jensen Aljoša Volčič
+ PDF Chat	Reconstruction of Convex Bodies from Brightness Functions	2003	Richard J. Gardner Peyman Milanfar
+ PDF Chat	The Brunn-Minkowski inequality	2002	Richard J. Gardner
+ PDF Chat	A Brunn-Minkowski inequality for the integer lattice	2001	Richard J. Gardner Paolo Gronchi
+	The Brunn–Minkowski Inequality, Minkowski's First Inequality, and Their Duals	2000	Richard J. Gardner Salvatore Vassallo
+	On the computational complexity of determining polyatomic structures by X-rays	2000	Richard J. Gardner Peter Gritzmann D. Prangenberg
+	Stability of Inequalities in the Dual Brunn-Minkowski Theory	1999	Richard J. Gardner Salvatore Vassallo
+ PDF Chat	An Analytic Solution to the Busemann-Petty Problem on Sections of Convex Bodies	1999	Richard J. Gardner Alexander Koldobsky Thomas Schlumprecht
+	An analytic solution to the Busemann-Petty problem on sections of convex bodies	1999	Richard J. Gardner Alexander Koldobsky Thomas Schlumprecht
+ PDF Chat	On the Determination of Star and Convex Bodies by Section Functions	1999	Richard J. Gardner Alessandro Soranzo Aljoša Volčič
+	An analytic solution to the Busemann-Petty problem	1999	Richard J. Gardner Alexander Koldobsky Thomas Schlumprecht
+ PDF Chat	p-Cross-section bodies	1999	Richard J. Gardner Apostolos Giannopoulos
+	An analytic solution to the Busemann-Petty problem on sections of convex bodies	1999	Richard J. Gardner Alexander Koldobsky Thomas Schlumprecht
+	Inequalities for dual isoperimetric deficits	1998	Richard J. Gardner Salvatore Vassallo
+	Affine inequalities and radial mean bodies	1998	Richard J. Gardner Gaoyong Zhang
+	Tomography of Convex and Star Bodies	1994	Richard J. Gardner Aljoša Volčič
+	Successive Determination and Verification of Polytopes by their X-Rays	1994	Richard J. Gardner Peter Gritzmann
+	A Positive Answer to the Busemann-Petty Problem in Three Dimensions	1994	Richard J. Gardner
+ PDF Chat	On the Busemann-Petty problem\\ concerning central sections\\ of centrally symmetric convex bodies	1994	Richard J. Gardner
+	On the Busemann-Petty problem concerning central sections of centrally symmetric convex bodies	1994	Richard J. Gardner
+ PDF Chat	Intersection bodies and the Busemann-Petty problem	1994	Richard J. Gardner
+ PDF Chat	Convex bodies with similar projections	1994	Richard J. Gardner Aljoša Volčič
+	On the Busemann-Petty problem concerning central sections of centrally symmetric convex bodies	1994	Richard J. Gardner
+	Determination of convex bodies by their brightness functions	1993	Richard J. Gardner Aljoša Volčič
+	Sets determined by finitely many X-rays	1992	Richard J. Gardner
+ PDF Chat	X-rays of polygons	1992	Richard J. Gardner
+ PDF Chat	The Banach-Tarski theorem on polygons, and the cancellation law	1990	Richard J. Gardner Miklós Laczkovich
+ PDF Chat	Relative width measures and the plank problem	1988	Richard J. Gardner
+	Bijections of #x211D; n onto itself	1988	Richard J. Gardner R. Daniel Mauldin
+	Chord Functions of Convex Bodies	1987	Richard J. Gardner
+	THE BANACH-TARSKI PARADOX (Encyclopedia of Mathematics and Its Applications, 24)	1986	Richard J. Gardner
+ PDF Chat	Convex bodies equidecomposable by locally discrete groups of isometries	1985	Richard J. Gardner
+ PDF Chat	A problem of Sallee on equidecomposable convex bodies	1985	Richard J. Gardner
+ PDF Chat	Decomposability of Radon measures	1984	Richard J. Gardner Washek F. Pfeffer
+	Conditions that imply a space is Radon	1984	Richard J. Gardner Washek F. Pfeffer
+	Borel Measures	1984	Richard J. Gardner Washek F. Pfeffer
+	Symmetrals and X-rays of planar convex bodies	1983	Richard J. Gardner
+ PDF Chat	On the Hausdorff dimension of a set of complex continued fractions	1983	Richard J. Gardner R. Daniel Mauldin
+ PDF Chat	Some Inequalities Related to Planar Convex Sets	1982	Richard J. Gardner Stanisław Kwapień D. P. Laurie
+ PDF Chat	A Note on Conditional Distributions and Orthogonal Measures	1982	Richard J. Gardner
+	The regularity of borel measures	1982	Richard J. Gardner
+	A counterexample to a ?simplex algorithm? for convex bodies	1981	S Gallivan Richard J. Gardner
+	Indicating cones and the intersection principle for tangential approximants in abstract multiplier rules	1981	D. H. Martin Richard J. Gardner G. G. Watkins
+ PDF Chat	Finite Borel measures on spaces of cardinality less than $\mathfrak{c}$	1981	Richard J. Gardner Gary Gruenhage
+	RELATION BETWEEN THE REGULARITY AND σ-FINITENESS OF RADON MEASURES	1980	Richard J. Gardner Washek F. Pfeffer
+	On Hammer's X-Ray Problem	1980	Richard J. Gardner Peter McMullen
+ PDF Chat	Some undecidability results concerning Radon measures	1980	Richard J. Gardner Washek F. Pfeffer
+	RESULTS AND CONJECTURES ON COVERING METRIC SPACES	1980	Richard J. Gardner
+	Are Diffused, Regular, Radon Measures σ-Finite?	1979	Richard J. Gardner Washek F. Pfeffer
+	Completeness and Weak Covering Properties, and Measure-Compactness	1978	Gary Gruenhage Richard J. Gardner
+ PDF Chat	Majorizing sequences and approximation	1976	Richard J. Gardner J. G. Hawkes
+	The Regularity of Borel Measures and Borel Measure-Compactness	1975	Richard J. Gardner
+	Approximating sequences and Hausdorff measure	1974	Richard J. Gardner

Common Coauthors

Coauthor	Papers Together
Paolo Gronchi	16
Daniel Hug	11
Wolfgang Weil	9
Markus Kiderlen	8
Gabriele Bianchi	8
Washek F. Pfeffer	6
Deping Ye	5
Aljoša Volčič	5
Stefano Campi	4
Thomas Schlumprecht	4
Sudan Xing	4
Artem Zvavitch	4
Alexander Koldobsky	4
Peyman Milanfar	3
Salvatore Vassallo	3
Thorsten Theobald	3
Paolo Dulio	3
Carla Peri	3
Eva B. Vedel Jensen	2
Peter Gritzmann	2
Vladyslav Yaskin	2
Gary Gruenhage	2
R. Daniel Mauldin	2
Dmitri Ryabogin	2
Chris Boothroyd	1
G. G. Watkins	1
Amyn Poonawala	1
Stefano Campi	1
Peter McMullen	1
Robert S. Pennington	1
J. G. Hawkes	1
Kees Joost Batenburg	1
Gaoyong Zhang	1
Asger Hobolth	1
Rafal E. Dunin‐Borkowski	1
David Hartenstine	1
Lukas Parapatits	1
Franz E. Schuster	1
Alessandro Soranzo	1
Dmitry Ryabogin	1
Stanisław Kwapień	1
D. Prangenberg	1
Miklós Laczkovich	1
Andreas Alpers	1
Stefan König	1
D. H. Martin	1
Apostolos Giannopoulos	1
S Gallivan	1
Vlad Yaskin	1
D. P. Laurie	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Convex Bodies: The Brunn–Minkowski Theory	1993	Rolf Schneider	39
+	Intersection bodies and dual mixed volumes	1988	Erwin Lutwak	26
+	A Positive Answer to the Busemann-Petty Problem in Three Dimensions	1994	Richard J. Gardner	21
+ PDF Chat	The Brunn-Minkowski inequality	2002	Richard J. Gardner	18
+	Tomography of Convex and Star Bodies	1994	Richard J. Gardner Aljoša Volčič	16
+ PDF Chat	Intersection bodies and the Busemann-Petty problem	1994	Richard J. Gardner	13
+	A Positive Solution to the Busemann-Petty Problem in \Bbb R 4	1999	Gaoyong Zhang	12
+ PDF Chat	Operations between sets in geometry	2013	Richard J. Gardner Daniel Hug Wolfgang Weil	11
+ PDF Chat	An Analytic Solution to the Busemann-Petty Problem on Sections of Convex Bodies	1999	Richard J. Gardner Alexander Koldobsky Thomas Schlumprecht	10
+ PDF Chat	Orlicz centroid bodies	2010	Erwin Lutwak Deane Yang Gaoyong Zhang	10
+	Convex Bodies The Brunn-MinkowskiTheory	2013	Rolf Schneider	10
+	Convex and Discrete Geometry	2007		10
+	Intersection Bodies and the Busemann-Petty Inequalities in ℝ 4	1994	Gaoyong Zhang	10
+	Convex and Discrete Geometry	2007	Peter M. Gruber	10
+	Measure Theory and Fine Properties of Functions	2018	Lawrence C. Evans Ronald F. Garzepy	9
+ PDF Chat	The Orlicz-Brunn-Minkowski theory: A general framework, additions, and inequalities	2014	Richard J. Gardner Daniel Hug Wolfgang Weil	8
+ PDF Chat	Problems on convex bodies	1956	Herbert Busemann C. M. Petty	7
+ PDF Chat	Polar Means of Convex Bodies and a Dual to the Brunn-Minkowski Theorem	1961	William J. Firey	7
+	On the Busemann‐Petty problem about convex, centrally symmetric bodies in	1992	Michael Papadimitrakis	7
+	A new ellipsoid associated with convex bodies	2000	Erwin Lutwak Deane Yang Gaoyong Zhang	7
+ PDF Chat	Rearrangements and Convexity of Level Sets in PDE	1985	Bernhard Kawohl	7
+	On the Busemann-Petty problem for perturbations of the ball	1991	Jean Bourgain	7
+ PDF Chat	The Brunn-Minkowski-Firey theory. I. Mixed volumes and the Minkowski problem	1993	Erwin Lutwak	7
+	The existence of a centrally symmetric convex body with central sections that are unexpectedly small	1975	D. G. Larman C. A. Rogers	7
+	Isoperimetric inequalities in mathematical physics	1951	George Pólya Gábor Szegő	7
+	Orlicz projection bodies	2009	Erwin Lutwak Deane Yang Gaoyong Zhang	7
+ PDF Chat	Lp Affine Isoperimetric Inequalities	2000	Erwin Lutwak Deane Yang Gaoyong Zhang	7
+	Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed n-dimensional space	2006	Vitali Milman Alain Pajor	6
+	The Brunn–Minkowski–Firey inequality for nonconvex sets	2011	Erwin Lutwak Deane Yang Gaoyong Zhang	6
+	A note on a problem of H. Busemann and C. M. Petty concerning sections of symmetric convex bodies	1990	Apostolos Giannopoulos	6
+	Geometric tomography and local stereology	2003	Richard J. Gardner Eva B. Vedel Jensen Aljoša Volčič	6
+	Symmetrization in geometry	2016	Gabriele Bianchi Richard J. Gardner Paolo Gronchi	5
+	Convex bodies with extremal volumes having prescribed brightness in finitely many directions	1995	Stefano Campi Andrea Colesanti Paolo Gronchi	5
+	The Cramer-Rao inequality for star bodies	2002	Erwin Lutwak Deane Yang Gaoyong Zhang	5
+	On Compactness in Spaces of Measures and Measurecompact Spaces	1974	Richard Haydon	5
+	Star Valuations and Dual Mixed Volumes	1996	Daniel A. Klain	5
+	Geometric Applications of Fourier Series and Spherical Harmonics	1996	H. Groemer	5
+	Universal approximation of symmetrizations by polarizations	2005	Jean Van Schaftingen	5
+ PDF Chat	Blaschke-Santaló inequalities	1997	Erwin Lutwak Gaoyong Zhang	5
+	Unsolved problems in geometry	1991	H. T. Croft K. J. Falconer Richard K. Guy	5
+ PDF Chat	On the $L_{p}$-Minkowski problem	2003	Erwin Lutwak Deane Yang Gaoyong Zhang	5
+ PDF Chat	An approach to symmetrization via polarization	1999	Friedemann Brock Alexander Yu. Solynin	5
+	The even Orlicz Minkowski problem	2010	Christoph Haberl Erwin Lutwak Deane Yang Gaoyong Zhang	5
+ PDF Chat	Explicit approximation of the symmetric rearrangement by polarizations	2009	Jean Van Schaftingen	5
+	When Inner Regularity of Borel Measures Implies Regularity	1978	Gary Gruenhage Washek F. Pfeffer	5
+	Isoperimetric inequalities and applications	1980	Catherine Bandle	5
+	Fourier Analysis in Convex Geometry	2005	Alexander Koldobsky	5
+ PDF Chat	Sharp Affine LP Sobolev Inequalities	2002	Erwin Lutwak Deane Yang Gaoyong Zhang	5
+	The Regularity of Borel Measures and Borel Measure-Compactness	1975	Richard J. Gardner	5
+	The generalized joint spectral radius. A geometric approach	1997	Vladimir Yu. Protasov	5