Abstract
We obtain an analogue of the classical "Four-Cones Coincidence Theorem" in Carnot groups, i.e we characterize intrinsic sub-manifolds by the coincidence of its lower and upper paratangent (and tangent, as well) cones
References
- J. P. Aubin, H. Frankowska: Set-Valued Analysis, Birkhäuser, Boston (1990).Google Scholar
- F. Bigolin, S. Nicolussi Golo: A historical account on characterizations of C 1 manifolds in Euclidean spaces by tangent cones, J. Math. Anal. Appl. 412(1) (2014) 63–76.https://doi.org/10.1016/j.jmaa.2013.10.035Google Scholar
- F. Bigolin, G. H. Greco: Geometric characterizations of C 1 manifolds in Euclidean spaces by tangent cones, J. Math. Anal. Appl. 396(1) (2012) 145–163.https://doi.org/10.1016/j.jmaa.2012.06.010Google Scholar
- G. Bouligand: Introduction à la Géométrie Infinitésimale Directe, Vuibert, Paris (1932).Google Scholar
- F. H. Clarke: Generalized gradients and applications, Trans. Amer. Math. Soc. 205 (1975) 247–262.https://doi.org/10.1090/S0002-9947-1975-0367131-6Google Scholar
- B. Cornet: Contributions à la Théorie Mathématique des Mécanismes Dynamiques d’Allocation des Ressources Thèse, Université de Paris IX, Paris (1981).Google Scholar
- S. Dolecki, G. H. Greco: Towards historical roots of necessary conditions of optimality: regula of Peano, Control Cybern. 36 (2007) 491–518.Google Scholar
- S. Dolecki, G. H. Greco: Tangengy vis-à-vis differentiability by Peano, Severi and Guareschi, J. Convex Analysis 18(2) (2011) 301–339.https://doi.org/10.68381/jca18017Google Scholar
- G. B. Folland, E. M. Stein: Hardy Spaces on Homogeneous Groups, Mathematical Notes 28, Princeton University Press, Princeton (1982).https://doi.org/10.1515/9780691222455Google Scholar
- B. Franchi, R. Serapioni, F. Serra Cassano: Regular hypersurfaces, intrinsic perimeter and implicit function theorem in Carnot groups, Commun. Anal. Geom. 11(5) (2003) 909–944.https://doi.org/10.4310/CAG.2003.v11.n5.a4Google Scholar
- N. G. Lloyd: Degree Theory, Cambridge Tracts in Mathematics 73, Cambridge University Press, Cambridge (1978).Google Scholar
- G. Peano: Applicazioni Geometriche del Calcolo Infinitesimale, Bocca, Torino (1887).https://doi.org/10.3792/chmm/1424377228Google Scholar
- F. Severi: Sulla differenziabilitá totale delle funzioni di piú variabili, Ann. Mat. Pura Appl., IV. Ser. 13 (1934) 1–35.https://doi.org/10.1007/BF02413430Google Scholar
- S. K. Vodopyanov: Differentiability of mappings in the geometry of Carnot manifolds, Sib. Math. J. 48(2) (2007) 197–213.https://doi.org/10.1007/s11202-007-0022-4Google Scholar
- S. K. Vodop’yanov, I. M. Pupyshev: Whitney-type theorems on the extension of functions on Carnot groups, Sib. Mat. Zh. 47(4) (2006) 731–752.https://doi.org/10.1007/s11202-006-0072-zGoogle Scholar
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Published by Heldermann Verlag, 2014. Rights now held by Banach Press.
