Download this article
 Download this article For screen
For printing
Recent Issues

Volume 30
Issue 2, 389–833
Issue 1, 1–388

Volume 29, 9 issues

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
 
Author index
To appear
 
Other MSP journals
Volume growth of Funk geometry and the flags of polytopes

Dmitry Faifman, Constantin Vernicos and Cormac Walsh

Geometry & Topology 29 (2025) 3773–3811
Bibliography
1 M Alexander, M Fradelizi, A Zvavitch, Polytopes of maximal volume product, Discrete Comput. Geom. 62 (2019) 583 MR3996937
2 G Berck, A Bernig, C Vernicos, Volume entropy of Hilbert geometries, Pacific J. Math. 245 (2010) 201 MR2608435
3 F Besau, C Schütt, E M Werner, Flag numbers and floating bodies, Adv. Math. 338 (2018) 912 MR3861719
4 D Burago, S Ivanov, On asymptotic volume of tori, Geom. Funct. Anal. 5 (1995) 800 MR1354290
5 G R Chambers, E Portnoy, A note on Kalai’s 3d Conjecture, preprint (2022) arXiv:2211.09215
6 D Faifman, A Funk perspective on billiards, projective geometry and Mahler volume, J. Differential Geom. 127 (2024) 161 MR4753501
7 M Fradelizi, M Meyer, Increasing functions and inverse Santaló inequality for unconditional functions, Positivity 12 (2008) 407 MR2421143
8 M Fradelizi, M Meyer, A Zvavitch, Volume product, from: "Harmonic analysis and convexity" (editors A Koldobsky, A Volberg), Adv. Anal. Geom. 9, De Gruyter (2023) 163 MR4654479
9 R Freij, M Henze, M W Schmitt, G M Ziegler, Face numbers of centrally symmetric polytopes produced from split graphs, Electron. J. Combin. 20 (2013) 32 MR3066371
10 G Kalai, The number of faces of centrally-symmetric polytopes, Graphs Combin. 5 (1989) 389 MR1554357
11 G Kalai, Challenges in discrete geometry, I: Convex polytopes, recorded lecture (2021)
12 B Klartag, Isotropic constants and Mahler volumes, Adv. Math. 330 (2018) 74 MR3787541
13 G A Margulis, Certain applications of ergodic theory to the investigation of manifolds of negative curvature, Funkcional. Anal. i Priložen. 3 (1969) 89 MR257933
14 M Meyer, Une caractérisation volumique de certains espaces normés de dimension finie, Israel J. Math. 55 (1986) 317 MR876398
15 M Meyer, S Reisner, On the volume product of polygons, Abh. Math. Semin. Univ. Hambg. 81 (2011) 93 MR2812036
16 P Pansu, Croissance des boules et des géodésiques fermées dans les nilvariétés, Ergodic Theory Dynam. Systems 3 (1983) 415 MR741395
17 S Reisner, Minimal volume-product in Banach spaces with a 1-unconditional basis, J. London Math. Soc. 36 (1987) 126 MR897680
18 R T Rockafellar, Convex analysis, 28, Princeton Univ. Press (1970) MR274683
19 L A Santaló, An affine invariant for convex bodies of n-dimensional space, Portugal. Math. 8 (1949) 155 MR39293
20 R Sanyal, A Werner, G M Ziegler, On Kalai’s conjectures concerning centrally symmetric polytopes, Discrete Comput. Geom. 41 (2009) 183 MR2471868
21 R Sanyal, M Winter, Kalai’s 3d conjecture for unconditional and locally anti-blocking polytopes, Proc. Amer. Math. Soc. 153 (2025) 279 MR4840276
22 C Schütt, The convex floating body and polyhedral approximation, Israel J. Math. 73 (1991) 65 MR1119928
23 M Senechal, editor, Shaping space: exploring polyhedra in nature, art, and the geometrical imagination, Springer (2013) MR3087288
24 C Vernicos, C Walsh, Flag-approximability of convex bodies and volume growth of Hilbert geometries, Ann. Sci. Éc. Norm. Supér. 54 (2021) 1297 MR4363244
25 C Vernicos, C Walsh, Asymptotic Santaló points of centro-affine and Funk geometry, in preparation (2025)