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We investigate the geometric and topological structure of equidistant decompositions of Riemannian manifolds.
Kapovitch, Vitali 1 ; Lytchak, Alexander 2
@article{GT_2022_26_6_a4, author = {Kapovitch, Vitali and Lytchak, Alexander}, title = {The structure of submetries}, journal = {Geometry & topology}, pages = {2649--2711}, publisher = {mathdoc}, volume = {26}, number = {6}, year = {2022}, url = {http://geodesic.mathdoc.fr/item/GT_2022_26_6_a4/} }
Kapovitch, Vitali; Lytchak, Alexander. The structure of submetries. Geometry & topology, Tome 26 (2022) no. 6, pp. 2649-2711. http://geodesic.mathdoc.fr/item/GT_2022_26_6_a4/
[1] FK–convex functions on metric spaces, Manuscripta Math. 110 (2003) 115 | DOI
, ,[2] Alexandrov geometry, preprint (2019)
, , ,[3] Smoothness of isometric flows on orbit spaces and applications, Transform. Groups 22 (2017) 1 | DOI
, ,[4] Calculus, heat flow and curvature-dimension bounds in metric measure spaces, from: "Proceedings of the International Congress of Mathematicians, I" (editors B Sirakov, P N d Souza, M Viana), World Sci. (2018) 301
,[5] DC calculus, Math. Z. 288 (2018) 1037 | DOI
, ,[6] Metric measure spaces with Riemannian Ricci curvature bounded from below, Duke Math. J. 163 (2014) 1405 | DOI
, , ,[7] Rectifiable sets in metric and Banach spaces, Math. Ann. 318 (2000) 527 | DOI
, ,[8] Sets with positive reach, Arch. Math. (Basel) 38 (1982) 54 | DOI
,[9] Submetries of three-dimensional forms of nonnegative curvature, Sibirsk. Mat. Zh. 28 (1987) 44
,[10] Generalized normal homogeneous spheres, Sibirsk. Mat. Zh. 54 (2013) 742
,[11] A metric characterization of Riemannian submersions, Ann. Global Anal. Geom. 18 (2000) 577 | DOI
, ,[12] Multidimensional generalized Riemannian spaces, from: "Geometry, IV" (editor Y G Reshetnyak), Encycl. Math. Sci. 70, Springer (1993) 165 | DOI
, ,[13] Finite homogeneous metric spaces, Sibirsk. Mat. Zh. 60 (2019) 973 | DOI
, ,[14] Introduction to compact transformation groups, 46, Academic (1972)
,[15] Higher torsion in H–spaces, Trans. Amer. Math. Soc. 108 (1963) 353 | DOI
,[16] A D Aleksandrov spaces with curvatures bounded below, Uspekhi Mat. Nauk 47 (1992) 3
, , ,[17] Nilpotent structures and invariant metrics on collapsed manifolds, J. Amer. Math. Soc. 5 (1992) 327 | DOI
, , ,[18] Rigidity theorems for submetries in positive curvature, Adv. Math. 289 (2016) 784 | DOI
, ,[19] Completely regular mappings, Fund. Math. 45 (1958) 103 | DOI
, ,[20] Curvature measures, Trans. Amer. Math. Soc. 93 (1959) 418 | DOI
,[21] Alexander duality and Hurewicz fibrations, Trans. Amer. Math. Soc. 327 (1991) 201 | DOI
,[22] The de Rham decomposition theorem for metric spaces, Geom. Funct. Anal. 18 (2008) 120 | DOI
, ,[23] Regular points of extremal subsets in Alexandrov spaces, preprint (2019)
,[24] Isometry groups of Alexandrov spaces, Bull. Lond. Math. Soc. 45 (2013) 567 | DOI
, ,[25] On quotients of spaces with Ricci curvature bounded below, J. Funct. Anal. 275 (2018) 1368 | DOI
, , , ,[26] Singular Riemannian foliations and applications to positive and non-negative curvature, J. Topol. 8 (2015) 603 | DOI
, ,[27] Gluing of multiple Alexandrov spaces, preprint (2020)
, ,[28] Differentiable classification of 4–manifolds with singular Riemannian foliations, Math. Ann. 363 (2015) 525 | DOI
, ,[29] A generalization of Berger’s rigidity theorem for positively curved manifolds, Ann. Sci. École Norm. Sup. 20 (1987) 227 | DOI
, ,[30] The boundary conjecture for leaf spaces, Ann. Inst. Fourier (Grenoble) 69 (2019) 2941
, , ,[31] Metric constraints on exotic spheres via Alexandrov geometry, J. Reine Angew. Math. 487 (1997) 201 | DOI
, ,[32] Restrictions on the geometry at infinity of nonnegatively curved manifolds, Duke Math. J. 78 (1995) 257 | DOI
, ,[33] Submetries vs. submersions, Rev. Mat. Iberoam. 27 (2011) 605 | DOI
, ,[34] Focal radius, rigidity, and lower curvature bounds, Proc. Lond. Math. Soc. 116 (2018) 1519 | DOI
, ,[35] Orientation and symmetries of Alexandrov spaces with applications in positive curvature, J. Geom. Anal. 27 (2017) 1636 | DOI
, ,[36] Regularity of limits of noncollapsing sequences of manifolds, Geom. Funct. Anal. 12 (2002) 121 | DOI
,[37] Restrictions on collapsing with a lower sectional curvature bound, Math. Z. 249 (2005) 519 | DOI
,[38] Remarks on manifolds with two-sided curvature bounds, Anal. Geom. Metr. Spaces 9 (2021) 53 | DOI
, ,[39] Metric-measure boundary and geodesic flow on Alexandrov spaces, J. Eur. Math. Soc. 23 (2021) 29 | DOI
, , ,[40] Rectifiable sets and coarea formula for metric-valued mappings, J. Funct. Anal. 254 (2008) 1410 | DOI
,[41] Nächste Punkte in der Riemannschen Geometrie, Math. Z. 176 (1981) 327 | DOI
,[42] Orbifolds from a metric viewpoint, Geom. Dedicata 209 (2020) 43 | DOI
,[43] Alexandrov regions, in preparation
, ,[44] Bipolar comparison, Geom. Funct. Anal. 29 (2019) 258 | DOI
, , ,[45] Quantitative estimates on the singular sets of Alexandrov spaces, Peking Math. J. 3 (2020) 203 | DOI
, ,[46] Allgemeine Theorie der Submetrien und verwandte mathematische Probleme, , Universität Bonn, Mathematisches Institut (2002)
,[47] Differentiation in metric spaces, Algebra i Analiz 16 (2004) 128
,[48] On the geometry of subsets of positive reach, Manuscripta Math. 115 (2004) 199 | DOI
,[49] Almost convex subsets, Geom. Dedicata 115 (2005) 201 | DOI
,[50] Open map theorem for metric spaces, Algebra i Analiz 17 (2005) 139
,[51] Rigidity of spherical buildings and joins, Geom. Funct. Anal. 15 (2005) 720 | DOI
,[52] Topological regularity of spaces with an upper curvature bound, J. Eur. Math. Soc. 24 (2022) 137 | DOI
, ,[53] Curvature explosion in quotients and applications, J. Differential Geom. 85 (2010) 117
, ,[54] On Hölder continuous Riemannian and Finsler metrics, Trans. Amer. Math. Soc. 358 (2006) 2917 | DOI
, ,[55] Notes on topological stability, Bull. Amer. Math. Soc. 49 (2012) 475 | DOI
,[56] A slice theorem for singular Riemannian foliations, with applications, Trans. Amer. Math. Soc. 371 (2019) 4931 | DOI
, ,[57] Laplacian algebras, manifold submetries and the inverse invariant theory problem, Geom. Funct. Anal. 30 (2020) 536 | DOI
, ,[58] Riemannian foliations, 73, Birkhäuser (1988) | DOI
,[59] Toward canonical convex functions in Alexandrov spaces, preprint (2019)
,[60] Alexandrov’s spaces with curvature bounded below, II, preprint (1991)
,[61] DC structure on Alexandrov space, preprint (1994)
,[62] Proof of the soul conjecture of Cheeger and Gromoll, J. Differential Geom. 40 (1994) 209
,[63] Extremal subsets in Aleksandrov spaces and the generalized Liberman theorem, Algebra i Analiz 5 (1993) 242
, ,[64] Quasigeodesics and gradient curves in Alexandrov spaces, preprint (1995)
, ,[65] Parallel transportation for Alexandrov space with curvature bounded below, Geom. Funct. Anal. 8 (1998) 123 | DOI
,[66] Semiconcave functions in Alexandrov’s geometry, from: "Surveys in differential geometry, XI : Metric and comparison geometry" (editors J Cheeger, K Grove), Surv. Differ. Geom. 11, International (2007) 137 | DOI
,[67] Clifford algebras and new singular Riemannian foliations in spheres, Geom. Funct. Anal. 24 (2014) 1660 | DOI
,[68] On the structure of sets with positive reach, Math. Nachr. 290 (2017) 1806 | DOI
, ,[69] Local triviality for Hurewicz fiberings of manifolds, Topology 3 (1965) 43 | DOI
,[70] Collapsing three-manifolds under a lower curvature bound, J. Differential Geom. 56 (2000) 1
, ,[71] Singular Riemannian foliations and isoparametric submanifolds, Milan J. Math. 78 (2010) 355 | DOI
,[72] Conditions for a mapping to have the slicing structure property, Pacific J. Math. 30 (1969) 549 | DOI
,[73] A duality theorem for Riemannian foliations in nonnegative sectional curvature, Geom. Funct. Anal. 17 (2007) 1297 | DOI
,[74] Collapsing and pinching under a lower curvature bound, Ann. of Math. 133 (1991) 317 | DOI
,[75] Collapsing 4–manifolds under a lower curvature bound, preprint (2012)
,