Volume 23, issue 6 (2019)

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

Volume 23
Issue 7, 3233–3749
Issue 6, 2701–3231
Issue 5, 2165–2700
Issue 4, 1621–2164
Issue 3, 1085–1619
Issue 2, 541–1084
Issue 1, 1–540

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
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Contact integral geometry and the Heisenberg algebra

Dmitry Faifman

Geometry & Topology 23 (2019) 3041–3110
Bibliography
1 A Abbondandolo, B Bramham, U L Hryniewicz, P A S Salomão, A systolic inequality for geodesic flows on the two-sphere, Math. Ann. 367 (2017) 701 MR3606452
2 S Alesker, Description of translation invariant valuations on convex sets with solution of P McMullen’s conjecture, Geom. Funct. Anal. 11 (2001) 244 MR1837364
3 S Alesker, The multiplicative structure on continuous polynomial valuations, Geom. Funct. Anal. 14 (2004) 1 MR2053598
4 S Alesker, Theory of valuations on manifolds, I : Linear spaces, Israel J. Math. 156 (2006) 311 MR2282381
5 S Alesker, Theory of valuations on manifolds, II, Adv. Math. 207 (2006) 420 MR2264077
6 S Alesker, Theory of valuations on manifolds, IV : New properties of the multiplicative structure, from: "Geometric aspects of functional analysis" (editors V D Milman, G Schechtman), Lecture Notes in Math. 1910, Springer (2007) 1 MR2347038
7 S Alesker, Valuations on manifolds and integral geometry, Geom. Funct. Anal. 20 (2010) 1073 MR2746948
8 S Alesker, A Bernig, The product on smooth and generalized valuations, Amer. J. Math. 134 (2012) 507 MR2905004
9 S Alesker, D Faifman, Convex valuations invariant under the Lorentz group, J. Differential Geom. 98 (2014) 183 MR3238311
10 S Alesker, J H G Fu, Theory of valuations on manifolds, III : Multiplicative structure in the general case, Trans. Amer. Math. Soc. 360 (2008) 1951 MR2366970
11 S Alesker, J H G Fu, Integral geometry and valuations, Springer (2014) MR3380549
12 J C Álvarez Paiva, Dual spheres have the same girth, Amer. J. Math. 128 (2006) 361 MR2214896
13 J C Álvarez Paiva, F Balacheff, Contact geometry and isosystolic inequalities, Geom. Funct. Anal. 24 (2014) 648 MR3192037
14 J C Álvarez Paiva, F Balacheff, K Tzanev, Isosystolic inequalities for optical hypersurfaces, Adv. Math. 301 (2016) 934 MR3539394
15 S Artstein-Avidan, R Karasev, Y Ostrover, From symplectic measurements to the Mahler conjecture, Duke Math. J. 163 (2014) 2003 MR3263026
16 S Artstein-Avidan, V Milman, Y Ostrover, The M–ellipsoid, symplectic capacities and volume, Comment. Math. Helv. 83 (2008) 359 MR2390048
17 A Bernig, A product formula for valuations on manifolds with applications to the integral geometry of the quaternionic line, Comment. Math. Helv. 84 (2009) 1 MR2466073
18 A Bernig, L Bröcker, Valuations on manifolds and Rumin cohomology, J. Differential Geom. 75 (2007) 433 MR2301452
19 A Bernig, D Faifman, Valuation theory of indefinite orthogonal groups, J. Funct. Anal. 273 (2017) 2167 MR3669033
20 A Bernig, J H G Fu, Hermitian integral geometry, Ann. of Math. 173 (2011) 907 MR2776365
21 A Bernig, J H G Fu, G Solanes, Integral geometry of complex space forms, Geom. Funct. Anal. 24 (2014) 403 MR3192033
22 A Bernig, G Solanes, Classification of invariant valuations on the quaternionic plane, J. Funct. Anal. 267 (2014) 2933 MR3255479
23 A Bernig, G Solanes, Kinematic formulas on the quaternionic plane, Proc. Lond. Math. Soc. 115 (2017) 725 MR3716941
24 A Bernig, F Voide, Spin-invariant valuations on the octonionic plane, Israel J. Math. 214 (2016) 831 MR3544703
25 S Caracciolo, A D Sokal, A Sportiello, Algebraic/combinatorial proofs of Cayley-type identities for derivatives of determinants and Pfaffians, Adv. in Appl. Math. 50 (2013) 474 MR3032306
26 S S Chern, R S Hamilton, On Riemannian metrics adapted to three-dimensional contact manifolds, from: "Workshop Bonn 1984" (editors F Hirzebruch, J Schwermer, S Suter), Lecture Notes in Math. 1111, Springer (1985) 279 MR797427
27 H Donnelly, Heat equation and the volume of tubes, Invent. Math. 29 (1975) 239 MR402832
28 D Faifman, An extension of Schäffer’s dual girth conjecture to Grassmannians, J. Differential Geom. 92 (2012) 201 MR2998671
29 D Faifman, Crofton formulas and indefinite signature, Geom. Funct. Anal. 27 (2017) 489 MR3655955
30 J H G Fu, T Wannerer, Riemannian curvature measures, Geom. Funct. Anal. 29 (2019) 343 MR3945834
31 I M Gelfand, M M Smirnov, Lagrangians satisfying Crofton formulas, Radon transforms, and nonlocal differentials, Adv. Math. 109 (1994) 188 MR1304752
32 E D Gluskin, Y Ostrover, Asymptotic equivalence of symplectic capacities, Comment. Math. Helv. 91 (2016) 131 MR3471939
33 D Gourevitch, S Sahi, E Sayag, Invariant functionals on Speh representations, Transform. Groups 20 (2015) 1023 MR3416438
34 V Guillemin, S Sternberg, Geometric asymptotics, 14, Amer. Math. Soc. (1977) MR0516965
35 H Hadwiger, Vorlesungen über Inhalt, Oberfläche und Isoperimetrie, Springer (1957) MR0102775
36 L Hörmander, The analysis of linear partial differential operators, I : Distribution theory and Fourier analysis, 256, Springer (1990) MR1065993
37 D A Klain, Even valuations on convex bodies, Trans. Amer. Math. Soc. 352 (2000) 71 MR1487620
38 A Koldobsky, D Ryabogin, A Zvavitch, Projections of convex bodies and the Fourier transform, Israel J. Math. 139 (2004) 361 MR2041799
39 J A C Kolk, V S Varadarajan, On the transverse symbol of vectorial distributions and some applications to harmonic analysis, Indag. Math. 7 (1996) 67 MR1621372
40 M Ludwig, M Reitzner, A characterization of affine surface area, Adv. Math. 147 (1999) 138 MR1725817
41 M Ludwig, M Reitzner, A classification of SL(n) invariant valuations, Ann. of Math. 172 (2010) 1219 MR2680490
42 P McMullen, Valuations and Euler-type relations on certain classes of convex polytopes, Proc. London Math. Soc. 35 (1977) 113 MR0448239
43 M Muro, Singular invariant hyperfunctions on the square matrix space and the alternating matrix space, Nagoya Math. J. 169 (2003) 19 MR1962523
44 Y Ostrover, When symplectic topology meets Banach space geometry, from: "Proceedings of the International Congress of Mathematicians" (editors S Y Jang, Y R Kim, D W Lee, I Ye), Kyung Moon Sa (2014) 959 MR3728647
45 V Ovsienko, Vector fields in the presence of a contact structure, Enseign. Math. 52 (2006) 215 MR2300607
46 R Ponge, The tangent groupoid of a Heisenberg manifold, Pacific J. Math. 227 (2006) 151 MR2247877
47 R S Ponge, Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds, 906, Amer. Math. Soc. (2008) MR2417549
48 B L Reinhart, The second fundamental form of a plane field, J. Differential Geom. 12 (1977) 619 MR512930
49 M Rumin, Formes différentielles sur les variétés de contact, J. Differential Geom. 39 (1994) 281 MR1267892
50 R Schneider, Convex bodies : the Brunn–Minkowski theory, 151, Cambridge Univ. Press (2014) MR3155183
51 G Solanes, T Wannerer, Integral geometry of exceptional spheres, preprint (2017) arXiv:1708.05861
52 H Tasaki, Generalization of Kähler angle and integral geometry in complex projective spaces, from: "Steps in differential geometry" (editors L Kozma, P T Nagy, L Tamássy), Inst. Math. Inform. (2001) 349 MR1859314
53 C Viterbo, Metric and isoperimetric problems in symplectic geometry, J. Amer. Math. Soc. 13 (2000) 411 MR1750956
54 H Weyl, On the volume of tubes, Amer. J. Math. 61 (1939) 461 MR1507388