Research/Publications
Preprints
- Narrowing the gaps of the missing Blaschke-Santaló diagrams
arXiv:2309.07772.
(with R. Brandenberg and K. von Dichter), arXiv:2306.11460.
Accepted/Published
- On diversities and finite dimensional Banach spaces
accepted on J. Conv. Anal. 2024.
- 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.
(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), in: Klartag B., Milman E. (eds) Geometric Aspects of Functional Analysis. 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.
(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.