Preprints:
Central diagonal section of gaussian n-cubes, with F. Fodor, arXiv:2511.01504.
A complete system of inequalities for the diameter, in-, and circumradius in the 3-dimensional Euclidean space with R. Brandenberg and M. Runge, arxiv:2509.05028.
From inequalities relating symmetrizations of convex bodies to the Diameter-width ratio for complete and pseudo-complete convex sets, with R. Brandenberg and K. von Dichter, arXiv:2306.11460.
Accepted/Published:
Geometry, Analysis and Convexity, RSME Springer Series (RSME, volume 17), 2026.
On diversities and finite dimensional Banach spaces, J. Conv. Anal. 32 (2025), no. 4, 1227--1240.
Tightening and reversing the arithmetic-harmonic mean inequality for symmetrizations of convex sets, with R. Brandenberg and K. von Dichter, Commun. Contemp. Math. 25 (2023), no. 9, 2250045.
Some remarks on Petty projection of log-concave functions, with L. Alves da Silva and R. Villa, J. Geom. Anal. 33 (2023), 260.
Behaviour of inradius, circumradius, and diameter in generalized Minkowski spaces, with R. Brandenberg, RACSAM 116 (2022).
Best approximation of functions by log-polynomials, with D. Alonso-Gutiérrez and R. Villa, J. Funct. Anal. 282 (2022), no. 5.
Relating Symmetrizations of Convex Bodies: Once More the Golden Ratio, with R. Brandenberg and K. von Dichter, Amer. Math. Month. 129 (2022), no. 4, 352--362.
Large signed subset sums, with G. Ambrus, Mathematika 67 (2021), no. 3, 579--595.
Estimating the average of functions with convexity properties by means of a new center, Ann. di Mat. Pura ed Appl. 200 (2021), 2285--2304.
Central diagonal sections of the n-cube, with F. A. Bartha and F. Fodor, Int. Math. Res. Not. 2021 (2021), no. 4, 2861--2881.
On the isodiametric and isominwidth inequalities for planar bisections, with A. Cañete, Rev. Mat. Iberoam. 37 (2021), no. 4, 1247--1275.
On the reverse isodiametric problem and Dvoretzky-Rogers-type volume bounds, with M. Schymura, RACSAM 114, 136 (2020).
On a generalization of the Hermite-Hadamard inequality and applications in convex geometry, Mediter. J. Math., 17 (2020), no. 5, 1--14.
An extension of Berwald's inequality and its relation to Zhang's inequality, with D. Alonso-Gutiérrez and J. Bernués, J. Math. Anal. Appl., 486 (2020), no. 1.
On large equilateral point-sets in normed spaces, Arch. Math., 114 (2020), 553--559, Corrigendum to Remark 2.2.
Zhang's inequality for log-concave functions, with D. Alonso-Gutiérrez and J. Bernués, Klartag B., Milman E. (eds) GAFA, Lecture Notes in Mathematics, vol 2256. Springer, Cham, 2020.
Rogers-Shephard and local Loomis-Whitney type inequalities, with D. Alonso-Gutiérrez, S. Artstein-Avidan, C. H. Jiménez and R. Villa, Math. Annalen, 374 (2019), no. 3-4, 1719--1771.
Uniqueness of circumcenters in generalized Minkowski spaces, with T. Jahn and C. Richter, J. Approx. Theory, 237 (2019), no. 1, 153--159.
Is a complete, reduced set necessarily of constant width?, with R. Brandenberg, T. Jahn and H. Martini, Adv. Geom., 19 (2019), no. 1, 31--40.
John's ellipsoid and the integral ratio of a log-concave function, with D. Alonso-Gutiérrez, C. H. Jiménez and R. Villa, J. Geom. Anal., 28 (2018), no. 2, 1182--1201.
Additive colourful Carathéodory type results with an application to radii, with M. Brugger, M. Fiedler and A. Kirschbaum, Lin. Alg. Appl., 554 (2018), no. 1, 342--357. Corrigendum to Conjecture 4.2.
Hunting for reduced polytopes, with T. Jahn, A. Polyanskii and G. Wachsmuth, Discrete Comput. Geom., 60 (2018), no. 3, 801--808.
On densities of lattice arrangements intersecting every i-dimensional affine subspace, with M. Schymura, Discr. Comput. Geom., 58 (2017), no. 3, 663--685.
Minkowski concentricity and complete simplices, with R. Brandenberg, J. Math. Anal. Appl., 454 (2017), no. 2, 981--994.
Tight bounds on discrete quantitative Helly numbers, with G. Averkov, I. Paschke, M. Schymura and S. Weltge, Adv. in Appl. Math., 89 (2017), 76--101.
Improving bounds for the Perel'man-Pukhov quotient for inner and outer radii, J. Convex Anal., 24 (2017), no. 4, 1099--1116.
The asymmetry of complete and constant width bodies in general normed spaces and the Jung constant, with R. Brandenberg, Israel J. Math., 218 (2017), no. 1, 489- -510.
A complete 3-dimensional Blaschke-Santaló diagram, with R. Brandenberg, Math. Ineq. Appl., 20 (2017), no. 2, 301--348.
A generalization of the discrete version of Minkowski's fundamental theorem, with M. Henze, Mathematika, 62 (2016), no. 3, 637--652.
Rogers-Shephard inequality for log-concave functions, with D. Alonso-Gutiérrez, C. H. Jiménez and R. Villa, J. Funct. Anal., 271 (2016), no. 11, 3269--3299.
On densities of lattice arrangements intersecting every i-dimensional affine subspace, with M. Henze, Oberwolfach Preprints, Mathematisches Forschungsinstitut Oberwolfach, 2016.
A pseudometric invariant under similarities in the hyperspace of non-degenerated compact convex sets of R^n, with N. Jonard-Pérez, Topol. Appl., 194 (2015), 125- -143.
Volume inequalities for the i-th-Convolution bodies, with D. Alonso-Gutiérrez and C. H. Jiménez, J. Math. Anal. Appl., 424 (2015), no. 1, 385--401.
Successive radii of families of convex bodies, with M. A. Hernández Cifre and A. Hinrichs, Bull. Austr. Math. Soc., 91 (2015), no. 1, 331--344.
A remark on perimeter-diameter and perimeter-circumradius inequalities under lattice constraints, with M. Henze, J. Geom., 106 (2015), no. 1, 75--83.
A generalization of the discrete version of Minkowski's fundamental theorem, with M. Henze, Oberwolfach Preprints, Mathematisches Forschungsinstitut Oberwolfach, 2014.
On the families of successive radii and the sum of convex sets, Beitr. Algebra Geom., 55 (2014), no. 2, 433--440.
On successive radii and p-sums of convex bodies, with M. A. Hernández Cifre, Adv. Geom., 14 (2014), no. 1, 117--128.
On the ratio between successive radii of a symmetric convex body, Math. Ineq. Appl., 16 (2013), no. 2, 569--576.
Successive radii and Minkowski addition, with M. A. Hernández Cifre, Monat. Math., 166 (2012), no. 3-4, 395--409.