Edit Profile (opens in new tab) Gronchi, Paolo Co-Author Distance Author ID: gronchi.paolo Published as: Gronchi, Paolo; Gronchi, P. External Links: MGP Documents Indexed: 35 Publications since 1993, including 1 Additional arXiv Preprint 2 Contributions as Editor · 1 Further Contribution Co-Authors: 14 Co-Authors with 34 Joint Publications 398 Co-Co-Authors all top 5 Co-Authors 4 single-authored 19 Campi, Stefano 11 Gardner, Richard J. 9 Bianchi, Gabriele 7 Colesanti, Andrea 3 Kiderlen, Markus 2 Longinetti, Marco 1 Artstein-Avidan, Shiri 1 Burchard, Almut 1 Del Lungo, Alberto 1 Gritzmann, Peter 1 Herman, Gabor T. 1 Hug, Daniel 1 Ludwig, Monika 1 Mussnig, Fabian 1 Salani, Paolo 1 Theobald, Thorsten 1 Volčič, Aljoša 1 Zong, Chuanming all top 5 Serials 4 Advances in Mathematics 4 Discrete & Computational Geometry 3 Indiana University Mathematics Journal 3 Transactions of the American Mathematical Society 2 Israel Journal of Mathematics 2 Geometriae Dedicata 2 Mathematika 1 Applicable Analysis 1 Journal of Mathematical Analysis and Applications 1 Beiträge zur Algebra und Geometrie 1 Archiv der Mathematik 1 Bulletin of the London Mathematical Society 1 Canadian Mathematical Bulletin 1 Proceedings of the American Mathematical Society 1 Rendiconti dell’Istituto di Matematica dell’Università di Trieste 1 Advances in Applied Mathematics 1 Linear Algebra and its Applications 1 Bollettino della Unione Matemàtica Italiana. Serie VII. A 1 Bollettino della Unione Matematica Italiana. Serie VIII. Sezione A. La Matematica nella Società e nella Cultura 1 Lecture Notes in Mathematics 1 Springer INdAM Series all top 5 Fields 34 Convex and discrete geometry (52-XX) 5 Measure and integration (28-XX) 3 General and overarching topics; collections (00-XX) 3 Combinatorics (05-XX) 2 Functional analysis (46-XX) 2 Geometry (51-XX) 2 Computer science (68-XX) 2 Biology and other natural sciences (92-XX) 1 Number theory (11-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Differential geometry (53-XX) 1 Probability theory and stochastic processes (60-XX) 1 Numerical analysis (65-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 30 Publications have been cited 456 times in 308 Documents Cited by ▼ Year ▼ The \(L^p\)-Busemann-Petty centroid inequality. Zbl 1002.52005 Campi, S.; Gronchi, P. 144 2002 A Brunn-Minkowski inequality for the integer lattice. Zbl 0977.52019 Gardner, R. J.; Gronchi, P. 44 2001 On the reverse \(L_p\)-Busemann-Petty centroid inequality. Zbl 1056.52005 Campi, Stefano; Gronchi, Paolo 44 2002 On volume product inequalities for convex sets. Zbl 1095.52002 Campi, Stefano; Gronchi, Paolo 32 2006 Sums, projections, and sections of lattice sets, and the discrete covariogram. Zbl 1093.52008 Gardner, Richard J.; Gronchi, Paolo; Zong, Chuanming 23 2005 Volume inequalities for \(L_p\)-zonotypes. Zbl 1117.52011 Campi, Stefano; Gronchi, Paolo 22 2006 Symmetrization in geometry. Zbl 1366.52003 Bianchi, Gabriele; Gardner, Richard J.; Gronchi, Paolo 22 2017 A note on Sylvester’s problem for random polytopes in a convex body. Zbl 0969.52001 Campi, Stefano; Colesanti, Andrea; Gronchi, Paolo 14 1999 Extremal convex sets for Sylvester–Busemann type functionals. Zbl 1090.52006 Campi, S.; Gronchi, P. 14 2006 Minimum problems for volumes of convex bodies. Zbl 0851.52002 Campi, Stefano; Colesanti, Andrea; Gronchi, Paolo 12 1996 Estimates of Loomis-Whitney type for intrinsic volumes. Zbl 1225.52005 Campi, Stefano; Gronchi, Paolo 12 2011 Reverse and dual Loomis-Whitney-type inequalities. Zbl 1335.52007 Campi, Stefano; Gardner, Richard J.; Gronchi, Paolo 11 2016 Convergence in shape of Steiner symmetrizations. Zbl 1290.52008 Bianchi, Gabriele; Burchard, Almut; Gronchi, Paolo; Volčič, Aljoša 10 2012 Steiner symmetrals and their distance from a ball. Zbl 1046.52003 Bianchi, Gabriele; Gronchi, Paolo 8 2003 On the reverse Loomis-Whitney inequality. Zbl 1400.52008 Campi, Stefano; Gritzmann, Peter; Gronchi, Paolo 6 2018 Affinely regular polygons as extremals of area functionals. Zbl 1155.52001 Gronchi, Paolo; Longinetti, Marco 4 2008 Convex bodies with extremal volumes having prescribed brightness in finitely many directions. Zbl 0838.52011 Campi, Stefano; Colesanti, Andrea; Gronchi, Paolo 4 1995 Shaking compact sets. Zbl 0982.52002 Campi, Stefano; Colesanti, Andrea; Gronchi, Paolo 3 2001 The blocking sets and the packing problem. Zbl 0787.05025 Gronchi, Paolo 3 1993 Lightness functions. Zbl 1261.52002 Campi, Stefano; Gardner, Richard J.; Gronchi, Paolo; Kiderlen, Markus 3 2012 Rearrangement and polarization. Zbl 1448.28001 Bianchi, Gabriele; Gardner, Richard J.; Gronchi, Paolo; Kiderlen, Markus 3 2020 Convergence of symmetrization processes. Zbl 1487.52005 Bianchi, Gabriele; Gardner, Richard J.; Gronchi, Paolo 3 2022 A proof of a Loomis-Whitney type inequality via optimal transport. Zbl 1407.52006 Campi, Stefano; Gronchi, Paolo; Salani, Paolo 3 2019 Volume inequalities for sets associated with convex bodies. Zbl 1124.52007 Campi, Stefano; Gronchi, Paolo 2 2006 Bodies of constant brightness. Zbl 0926.52011 Gronchi, Paolo 2 1998 Blaschke-decomposable convex bodies. Zbl 0926.52005 Campi, Stefano; Colesanti, Andrea; Gronchi, Paolo 2 1998 On projection bodies of order one. Zbl 1175.52009 Campi, Stefano; Gronchi, Paolo 2 2009 Full rotational symmetry from reflections or rotational symmetries in finitely many subspaces. Zbl 07525032 Bianchi, Gabriele; Gardner, Richard J.; Gronchi, Paolo 2 2022 Affinely regular polygons as extremals of area functionals. Reprinted from the journal Discrete & Computational Geometry 39, No. 1-3 (2008). Zbl 1177.52005 Gronchi, Paolo; Longinetti, Marco 1 2009 Characterizations of Miquelian Laguerre planes. (Charakterisierungen Miquelscher Laguerre-Ebenen.) Zbl 0799.51004 Gronchi, Paolo 1 1994 Convergence of symmetrization processes. Zbl 1487.52005 Bianchi, Gabriele; Gardner, Richard J.; Gronchi, Paolo 3 2022 Full rotational symmetry from reflections or rotational symmetries in finitely many subspaces. Zbl 07525032 Bianchi, Gabriele; Gardner, Richard J.; Gronchi, Paolo 2 2022 Rearrangement and polarization. Zbl 1448.28001 Bianchi, Gabriele; Gardner, Richard J.; Gronchi, Paolo; Kiderlen, Markus 3 2020 A proof of a Loomis-Whitney type inequality via optimal transport. Zbl 1407.52006 Campi, Stefano; Gronchi, Paolo; Salani, Paolo 3 2019 On the reverse Loomis-Whitney inequality. Zbl 1400.52008 Campi, Stefano; Gritzmann, Peter; Gronchi, Paolo 6 2018 Symmetrization in geometry. Zbl 1366.52003 Bianchi, Gabriele; Gardner, Richard J.; Gronchi, Paolo 22 2017 Reverse and dual Loomis-Whitney-type inequalities. Zbl 1335.52007 Campi, Stefano; Gardner, Richard J.; Gronchi, Paolo 11 2016 Convergence in shape of Steiner symmetrizations. Zbl 1290.52008 Bianchi, Gabriele; Burchard, Almut; Gronchi, Paolo; Volčič, Aljoša 10 2012 Lightness functions. Zbl 1261.52002 Campi, Stefano; Gardner, Richard J.; Gronchi, Paolo; Kiderlen, Markus 3 2012 Estimates of Loomis-Whitney type for intrinsic volumes. Zbl 1225.52005 Campi, Stefano; Gronchi, Paolo 12 2011 On projection bodies of order one. Zbl 1175.52009 Campi, Stefano; Gronchi, Paolo 2 2009 Affinely regular polygons as extremals of area functionals. Reprinted from the journal Discrete & Computational Geometry 39, No. 1-3 (2008). Zbl 1177.52005 Gronchi, Paolo; Longinetti, Marco 1 2009 Affinely regular polygons as extremals of area functionals. Zbl 1155.52001 Gronchi, Paolo; Longinetti, Marco 4 2008 On volume product inequalities for convex sets. Zbl 1095.52002 Campi, Stefano; Gronchi, Paolo 32 2006 Volume inequalities for \(L_p\)-zonotypes. Zbl 1117.52011 Campi, Stefano; Gronchi, Paolo 22 2006 Extremal convex sets for Sylvester–Busemann type functionals. Zbl 1090.52006 Campi, S.; Gronchi, P. 14 2006 Volume inequalities for sets associated with convex bodies. Zbl 1124.52007 Campi, Stefano; Gronchi, Paolo 2 2006 Sums, projections, and sections of lattice sets, and the discrete covariogram. Zbl 1093.52008 Gardner, Richard J.; Gronchi, Paolo; Zong, Chuanming 23 2005 Steiner symmetrals and their distance from a ball. Zbl 1046.52003 Bianchi, Gabriele; Gronchi, Paolo 8 2003 The \(L^p\)-Busemann-Petty centroid inequality. Zbl 1002.52005 Campi, S.; Gronchi, P. 144 2002 On the reverse \(L_p\)-Busemann-Petty centroid inequality. Zbl 1056.52005 Campi, Stefano; Gronchi, Paolo 44 2002 A Brunn-Minkowski inequality for the integer lattice. Zbl 0977.52019 Gardner, R. J.; Gronchi, P. 44 2001 Shaking compact sets. Zbl 0982.52002 Campi, Stefano; Colesanti, Andrea; Gronchi, Paolo 3 2001 A note on Sylvester’s problem for random polytopes in a convex body. Zbl 0969.52001 Campi, Stefano; Colesanti, Andrea; Gronchi, Paolo 14 1999 Bodies of constant brightness. Zbl 0926.52011 Gronchi, Paolo 2 1998 Blaschke-decomposable convex bodies. Zbl 0926.52005 Campi, Stefano; Colesanti, Andrea; Gronchi, Paolo 2 1998 Minimum problems for volumes of convex bodies. Zbl 0851.52002 Campi, Stefano; Colesanti, Andrea; Gronchi, Paolo 12 1996 Convex bodies with extremal volumes having prescribed brightness in finitely many directions. Zbl 0838.52011 Campi, Stefano; Colesanti, Andrea; Gronchi, Paolo 4 1995 Characterizations of Miquelian Laguerre planes. (Charakterisierungen Miquelscher Laguerre-Ebenen.) Zbl 0799.51004 Gronchi, Paolo 1 1994 The blocking sets and the packing problem. Zbl 0787.05025 Gronchi, Paolo 3 1993 all cited Publications top 5 cited Publications all top 5 Cited by 285 Authors 17 Leng, Gangsong 15 Gronchi, Paolo 12 Wang, Weidong 11 Bianchi, Gabriele 11 Campi, Stefano 10 Böröczky, Karoly jun. 10 Gardner, Richard J. 10 Yang, Deane 10 Zhang, Gaoyong 9 Haberl, Christoph 9 Huang, Qingzhong 9 Xiong, Ge 8 Li, Aijun 8 Lin, Youjiang 8 Lutwak, Erwin 7 Colesanti, Andrea 7 Ludwig, Monika 7 Saroglou, Christos 7 Schuster, Franz E. 7 Yepes Nicolás, Jesús 6 Feng, Yibin 6 He, Binwu 6 Iglesias, David 6 Lucas, Eduardo 6 Meyer, Mathieu 6 Pivovarov, Peter 6 Wang, Wei 6 Xi, Dongmeng 6 Zvavitch, Artem 5 Jiménez, Carlos Hugo 5 Kiderlen, Markus 5 Paouris, Grigoris 5 Parapatits, Lukas 5 Serra, Oriol 4 Alonso-Gutiérrez, David 4 Averkov, Gennadiy 4 Chen, Fangwei 4 Fradelizi, Matthieu 4 Guo, Lujun 4 Haddad, Julián E. 4 Hernández Cifre, María A. 4 Montenegro, Marcos 4 Reisner, Shlomo 4 Si, Lin 4 Wu, Denghui 4 Wu, Yuchi 4 Yang, Congli 4 Zhang, Zengle 4 Zhou, Jiazu 4 Zhu, Baocheng 4 Zhu, Guangxian 3 Abardia-Evéquoz, Judit 3 Alexander, Matthew 3 Artstein-Avidan, Shiri 3 Gómez, Eugenia Saorín 3 Grynkiewicz, David J. 3 Henk, Martin 3 Klain, Daniel A. 3 Liu, Lijuan 3 Lv, Songjun 3 Nguyễn Văn Hoàng 3 Stanchescu, Yonutz V. 3 Werner, Elisabeth M. 3 Ye, Deping 3 Zhao, Changjian 3 Zhou, Yanping 2 Barlotti, Adriano 2 Bezdek, Károly 2 Brazitikos, Silouanos 2 Bu, Zhenhui 2 Cheung, Wingsum 2 Du, Changmin 2 Fang, Niufa 2 Freiman, Gregory A. 2 Freyer, Ansgar 2 Hack, Thomas-Paul 2 Horváth, Ákos G. 2 Hu, Jiaqi 2 Huicochea, Mario 2 Jin, Hailin 2 Kousholt, Astrid 2 Langfeld, Barbara 2 Lángi, Zsolt 2 Li, Tian 2 Lu, Jian 2 Madiman, Mokshay M. 2 Melbourne, James 2 Nagy, Ábris 2 Rebollo Bueno, Jesus 2 Ruzsa, Imre Z. 2 Tang, Zhongwen 2 Ulivelli, Jacopo 2 Vincze, Csaba 2 Volčič, Aljoša 2 Wang, Liyao 2 Woo, Jae Oh 2 Xiao, Jie 2 Xu, Wenxue 2 Yaskin, Vladyslav 2 Yu, Wuyang ...and 185 more Authors all top 5 Cited in 101 Serials 34 Advances in Mathematics 22 Advances in Applied Mathematics 15 Discrete & Computational Geometry 12 Proceedings of the American Mathematical Society 11 Journal of Mathematical Analysis and Applications 10 Transactions of the American Mathematical Society 10 The Journal of Geometric Analysis 9 Mathematika 8 Journal of Functional Analysis 7 Mathematische Annalen 7 Calculus of Variations and Partial Differential Equations 6 Israel Journal of Mathematics 6 Geometriae Dedicata 6 Journal of Inequalities and Applications 5 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 5 Journal of Mathematical Inequalities 4 Monatshefte für Mathematik 4 Results in Mathematics 4 Journal of the American Mathematical Society 4 SIAM Journal on Discrete Mathematics 4 Acta Mathematica Sinica. English Series 3 Discrete Mathematics 3 Archiv der Mathematik 3 Glasgow Mathematical Journal 3 Journal of Geometry 3 Journal of the London Mathematical Society. Second Series 3 Indagationes Mathematicae. New Series 3 Wuhan University Journal of Natural Sciences (WUJNS) 3 Journal of the European Mathematical Society (JEMS) 3 Communications in Contemporary Mathematics 2 Rocky Mountain Journal of Mathematics 2 Bulletin of the London Mathematical Society 2 Indiana University Mathematics Journal 2 Journal of Statistical Planning and Inference 2 Quaestiones Mathematicae 2 European Journal of Combinatorics 2 Forum Mathematicum 2 Aequationes Mathematicae 2 Mathematical Inequalities & Applications 2 Advances in Geometry 2 Science China. Mathematics 2 Journal of Function Spaces 1 Advances in Applied Probability 1 Applicable Analysis 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Studia Mathematica 1 The Mathematical Intelligencer 1 American Journal of Mathematics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 The Annals of Probability 1 The Annals of Statistics 1 Annales Polonici Mathematici 1 Canadian Journal of Mathematics 1 Canadian Mathematical Bulletin 1 Collectanea Mathematica 1 Journal of Combinatorial Theory. Series A 1 Journal of Differential Equations 1 Journal of Differential Geometry 1 Journal of Number Theory 1 Mathematische Zeitschrift 1 Siberian Mathematical Journal 1 Theoretical Computer Science 1 Combinatorica 1 Applied Mathematics and Mechanics. (English Edition) 1 Acta Mathematica Hungarica 1 Acta Applicandae Mathematicae 1 Revista Matemática Iberoamericana 1 Applied Mathematics Letters 1 The Annals of Applied Probability 1 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Expositiones Mathematicae 1 Journal of Nonlinear Science 1 Combinatorics, Probability and Computing 1 The Electronic Journal of Combinatorics 1 Mathematical Problems in Engineering 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Taiwanese Journal of Mathematics 1 Journal of Shanghai University 1 Annals of Mathematics. Second Series 1 Fundamenta Informaticae 1 Discrete and Continuous Dynamical Systems. Series B 1 Journal of the Australian Mathematical Society 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Advanced Nonlinear Studies 1 Journal of Algebra and its Applications 1 Analysis in Theory and Applications 1 Mediterranean Journal of Mathematics 1 Foundations of Physics 1 Oberwolfach Reports 1 Contributions to Discrete Mathematics 1 Journal of Nonlinear Science and Applications 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Journal of Classical Analysis 1 Annales Mathématiques du Québec 1 Analysis and Geometry in Metric Spaces 1 Arnold Mathematical Journal 1 Open Mathematics 1 Journal de l’École Polytechnique – Mathématiques ...and 1 more Serials all top 5 Cited in 41 Fields 270 Convex and discrete geometry (52-XX) 28 Functional analysis (46-XX) 26 Probability theory and stochastic processes (60-XX) 21 Real functions (26-XX) 19 Number theory (11-XX) 17 Differential geometry (53-XX) 13 Partial differential equations (35-XX) 12 Combinatorics (05-XX) 11 Geometry (51-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 7 Measure and integration (28-XX) 7 Information and communication theory, circuits (94-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 6 Computer science (68-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Statistics (62-XX) 4 Operator theory (47-XX) 3 Group theory and generalizations (20-XX) 3 Potential theory (31-XX) 3 Integral transforms, operational calculus (44-XX) 3 Numerical analysis (65-XX) 2 General and overarching topics; collections (00-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Functions of a complex variable (30-XX) 2 Difference and functional equations (39-XX) 2 Optics, electromagnetic theory (78-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Biology and other natural sciences (92-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Algebraic geometry (14-XX) 1 Associative rings and algebras (16-XX) 1 Topological groups, Lie groups (22-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Ordinary differential equations (34-XX) 1 Abstract harmonic analysis (43-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of particles and systems (70-XX) 1 Quantum theory (81-XX) Citations by Year