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

Volume 30
Issue 5, 1611–2042
Issue 4, 1203–1610
Issue 3, 835–1201
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)