Duke Mathematical Journal

Tubular neighborhoods in Euclidean spaces

Joseph Howland Guthrie Fu

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Duke Math. J. Volume 52, Number 4 (1985), 1025-1046.

Dates
First available: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077304735

Mathematical Reviews number (MathSciNet)
MR816398

Zentralblatt MATH identifier
0592.52002

Digital Object Identifier
doi:10.1215/S0012-7094-85-05254-8

Subjects
Primary: 57N40: Neighborhoods of submanifolds
Secondary: 52A15: Convex sets in 3 dimensions (including convex surfaces) [See also 53A05, 53C45]

Citation

Fu, Joseph Howland Guthrie. Tubular neighborhoods in Euclidean spaces. Duke Mathematical Journal 52 (1985), no. 4, 1025--1046. doi:10.1215/S0012-7094-85-05254-8. http://projecteuclid.org/euclid.dmj/1077304735.


Export citation

References

  • [1] V. Bangert, Sets with positive reach, Arch. Math. (Basel) 38 (1982), no. 1, 54–57.
  • [2] V. Bangert, Analytische Eigenschaften konvexer Funktionen auf Riemannschen Mannigfaltigkeiten, J. Reine Angew. Math. 307/308 (1979), 309–324.
  • [3] T. Bonneson and W. Fenchel, Konvexer Korper, Chelsea, New York, reprint, 1971.
  • [4] M. Brown, Sets of constant distance from a planar set, Michigan Math. J. 19 (1972), 321–323.
  • [5] Frank H. Clarke, Optimization and nonsmooth analysis, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons Inc., New York, 1983.
  • [6] F. H. Clarke, Generalized gradients and applications, Trans. Amer. Math. Soc. 205 (1975), 247–262.
  • [7] P. Cohen, Decision procedures for real and $p$-adic fields, Comm. Pure Appl. Math. 22 (1969), 131–151.
  • [8] R. M. Dudley, On second derivatives of convex functions, Math. Scand. 41 (1977), no. 1, 159–174.
  • [9] R. M. Dudley, Acknowledgment of priority: “On second derivatives of convex functions”, Math. Scand. 46 (1980), no. 1, 61.
  • [10] H. Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York Inc., New York, 1969.
  • [11] H. Federer, Curvature measures, Trans. Amer. Math. Soc. 93 (1959), 418–491.
  • [12] S. Ferry, When $\epsilon$-boundaries are manifolds, Fund. Math. 90 (1975/76), no. 3, 199–210.
  • [13] J. H. G. Fu, Tubular neighborhoods of planner sets, Thesis, MIT, 1984.
  • [14] R. Gariepy and W. D. Pepe, On the level sets of a distance function in a Minkowski space, Proc. Amer. Math. Soc. 31 (1972), 255–259.
  • [15] H. Lebesgue, En marge du calcul des variations. Une introduction au calcul des variations et aux inégalités géométriques, Monographies de “L'Enseignement Mathématique”, No. 12, Inst. de Maths., Université, Geneva, 1963.
  • [16] P.-L. Lions, Generalized solutions of Hamilton-Jacobi equations, Research Notes in Mathematics, vol. 69, Pitman (Advanced Publishing Program), Boston, Mass., 1982.
  • [17] P.-L. Lions, Letter dated February 19, 1983.
  • [18] B. Mandelbrot, Fractals, W. H. Freeman Co., San Francisco, 1977.
  • [19] A. P. Morse, The behavior of a function on its critical set, Ann. of Math. 40 (1939), 62–70.
  • [20] Yu. G. Reshetnyak, Generalized derivatives and differentiability almost everywhere, Math. USSR Sbornik 4 (1968), 293–302.
  • [21] R. T. Rockafellar, Convex analysis, Princeton Mathematical Series, No. 28, Princeton University Press, Princeton, N.J., 1970.
  • [22] L. A. Santalo, Integral geometry and geometric probability, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1976.
  • [23] L. Schwartz, Théorie des distributions, Publications de l'Institut de Mathématique de l'Université de Strasbourg, No. IX-X. Nouvelle édition, entiérement corrigée, refondue et augmentée, Hermann, Paris, 1966.
  • [24] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970.
  • [25] H. Tietze, Eine charakteristische Eigenschaft der abgeschlossenen konvexen Punktmengen, Math. Ann. 99 (1928), 394.
  • [26] H. Weyl, On the volume of tubes., Am. J. Math. 61 (1939), 461–472.
  • [27] H. Whitney, A function not constant on a connected set of critical points, Duke Math. J. 1 (1935), 514–517.
  • [28] H. Whitney, Elementary structure of real algebraic varieties, Ann. of Math. (2) 66 (1957), 545–556.
  • [29] Y. Yomdin, The geometry of critical and near-critical values of differentiable mappings, Math. Ann. 264 (1983), no. 4, 495–515.