Geometry & Topology Volume 30, issue 7 (2026)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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The Weyl tube theorem for Kähler manifolds

Andreas Bernig, Joseph H G Fu, Gil Solanes and Thomas Wannerer

Geometry & Topology 30 (2026) 2713–2772

DOI: 10.2140/gt.2026.30.2713

Bibliography

1	J Abardia, E Gallego, G Solanes, The Gauss–Bonnet theorem and Crofton-type formulas in complex space forms, Israel J. Math. 187 (2012) 287 MR2891707
2	M Aigner, Catalan-like numbers and determinants, J. Combin. Theory Ser. A 87 (1999) 33 MR1698277
3	S Alesker, Description of translation invariant valuations on convex sets with solution of P McMullen’s conjecture, Geom. Funct. Anal. 11 (2001) 244 MR1837364
4	S Alesker, Hard Lefschetz theorem for valuations, complex integral geometry, and unitarily invariant valuations, J. Differential Geom. 63 (2003) 63 MR2015260
5	S Alesker, Theory of valuations on manifolds, I : Linear spaces, Israel J. Math. 156 (2006) 311 MR2282381
6	S Alesker, Theory of valuations on manifolds, II, Adv. Math. 207 (2006) 420 MR2264077
7	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
8	S Alesker, Valuations on manifolds and integral geometry, Geom. Funct. Anal. 20 (2010) 1073 MR2746948
9	S Alesker, Some conjectures on intrinsic volumes of Riemannian manifolds and Alexandrov spaces, Arnold Math. J. 4 (2018) 1 MR3810565
10	S Alesker, On convergence of intrinsic volumes of Riemannian manifolds, J. Geom. 113 (2022) 23 MR4393073
11	S Alesker, A Bernig, The product on smooth and generalized valuations, Amer. J. Math. 134 (2012) 507 MR2905004
12	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
13	S Alesker, M G Katz, R Prosanov, New invariants of Gromov–Hausdorff limits of Riemannian surfaces with curvature bounded below, Geom. Dedicata 217 (2023) 12 MR4535845
14	M Atiyah, R Bott, V K Patodi, On the heat equation and the index theorem, Invent. Math. 19 (1973) 279 MR650828
15	A Bernig, Curvature tensors of singular spaces, Differential Geom. Appl. 24 (2006) 191 MR2198794
16	A Bernig, Unitarily invariant valuations and Tutte’s sequence, Proc. Amer. Math. Soc. 149 (2021) 829 MR4198087
17	A Bernig, L Bröcker, Valuations on manifolds and Rumin cohomology, J. Differential Geom. 75 (2007) 433 MR2301452
18	A Bernig, J H G Fu, Hermitian integral geometry, Ann. of Math. (2) 173 (2011) 907 MR2776365
19	A Bernig, J H G Fu, G Solanes, Integral geometry of complex space forms, Geom. Funct. Anal. 24 (2014) 403 MR3192033
20	A Bernig, J H G Fu, G Solanes, Dual curvature measures in Hermitian integral geometry, from: "Analytic aspects of convexity" (editors G Bianchi, A Colesanti, P Gronchi), Springer INdAM 25, Springer (2018) 1 MR3753099
21	A Bernig, D Faifman, G Solanes, Uniqueness of curvature measures in pseudo-Riemannian geometry, J. Geom. Anal. 31 (2021) 11819 MR4322553
22	A Bernig, D Faifman, G Solanes, Crofton formulas in pseudo-Riemannian space forms, Compos. Math. 158 (2022) 1935 MR4502598
23	A Bernig, D Faifman, G Solanes, Curvature measures of pseudo-Riemannian manifolds, J. Reine Angew. Math. 788 (2022) 77 MR4445545
24	K J Böröczky, M Domokos, G Solanes, Dimension of the space of unitary equivariant translation invariant tensor valuations, J. Funct. Anal. 280 (2021) 108862 MR4181164
25	D Bump, Lie groups, 225, Springer (2013) MR3136522
26	S s Chern, On the curvatura integra in a Riemannian manifold, Ann. of Math. (2) 46 (1945) 674 MR14760
27	H Donnelly, Heat equation and the volume of tubes, Invent. Math. 29 (1975) 239 MR402832
28	H Federer, Curvature measures, Trans. Amer. Math. Soc. 93 (1959) 418 MR110078
29	J H G Fu, Curvature measures of subanalytic sets, Amer. J. Math. 116 (1994) 819 MR1287941
30	J H G Fu, Structure of the unitary valuation algebra, J. Differential Geom. 72 (2006) 509 MR2219942
31	J H G Fu, Intersection theory and the Alesker product, Indiana Univ. Math. J. 65 (2016) 1347 MR3549204
32	J H G Fu, T Wannerer, Riemannian curvature measures, Geom. Funct. Anal. 29 (2019) 343 MR3945834
33	J H G Fu, D Pokorný, J Rataj, Kinematic formulas for sets defined by differences of convex functions, Adv. Math. 311 (2017) 796 MR3628231
34	W Fulton, Young tableaux: with applications to representation theory and geometry, 35, Cambridge Univ. Press (1997) MR1464693
35	W Fulton, Intersection theory, 2, Springer (1998) MR1644323
36	R L Graham, D E Knuth, O Patashnik, Concrete mathematics: a foundation for computer science, Addison-Wesley (1994) MR1397498
37	A Gray, Some relations between curvature and characteristic classes, Math. Ann. 184 (1969/70) 257 MR261492
38	A Gray, Tubes, 221, Birkhäuser (2004) MR2024928
39	R Howard, The kinematic formula in Riemannian homogeneous spaces, 509, Amer. Math. Soc. (1993) MR1169230
40	H Park, Kinematic formulas for the real subspaces of complex space forms of dimension 2 and 3, PhD thesis, University of Georgia (2002)
41	D Pokorný, J Rataj, Normal cycles and curvature measures of sets with d.c. boundary, Adv. Math. 248 (2013) 963 MR3107534
42	G de Rham, Differentiable manifolds: forms, currents, harmonic forms, 266, Springer (1984) MR760450
43	M Rumin, Formes différentielles sur les variétés de contact, J. Differential Geom. 39 (1994) 281 MR1267892
44	L A Santaló, Integral geometry and geometric probability, 1, Addison-Wesley (1976) MR433364
45	T Shifrin, The kinematic formula in complex integral geometry, Trans. Amer. Math. Soc. 264 (1981) 255 MR603763
46	M Sitaramayya, Curvature tensors in Kaehler manifolds, Trans. Amer. Math. Soc. 183 (1973) 341 MR322722
47	G Solanes, T Wannerer, Integral geometry of exceptional spheres, J. Differential Geom. 117 (2021) 137 MR4195754
48	T Wannerer, Classification of angular curvature measures and a proof of the angularity conjecture, Amer. J. Math. 144 (2022) 1331 MR4494184
49	H Weyl, On the volume of tubes, Amer. J. Math. 61 (1939) 461 MR1507388