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A note on the existence of horizontal envelopes in the 3D-Heisenberg group

Yen-Chang Huang
대한수학회 (The Korean Mathematical Society)|2020.03|대한수학회지 (Journal of the KMS)|제57권 제2호|pp. 415-427|DOI 10.4134/JKMS.j190098

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키워드

Sub-Riemannian manifoldspseudo-hermitian geometryenvelo\-pes
주제분류수학

초록

By using the support functions on the $xy$-plane, we show the necessary and sufficient conditions for the existence of envelopes of horizontal lines in the 3D-Heisenberg group. A method to construct horizontal envelopes from the given ones is also derived, and we classify the solutions satisfying the construction.

Abstract

By using the support functions on the $xy$-plane, we show the necessary and sufficient conditions for the existence of envelopes of horizontal lines in the 3D-Heisenberg group. A method to construct horizontal envelopes from the given ones is also derived, and we classify the solutions satisfying the construction.

참고문헌 (27)

  1. V. I. Arnold, "Graduate Texts in Mathematics, 60" (1989), Springer-Verlag
  2. V. I. Arnold, "Mathematics and its Applications (Soviet Series), 62", pp.62~ (1990), Kluwer Academic Publishers Group
  3. V. I. Arnold, "Singularity Theory. II, Dynamical Systems VIII", Encyclopaedia Math. Sci., 39 (1993), Springer-Verlag
  4. V. I. Arnold, "Monographs in Mathematics", pp.82~ (1985), Birkhauser Boston, Inc
  5. J. -D. Boissonnat, "On-line construction of the upper envelope of triangles and surface patches in three dimensions", Comput. Geom., 5(6), pp.303~320 (1996)[DOI]
  6. O. Calin, "Geometric mechanics on the Heisenberg group", Bull. Inst. Math. Acad. Sinica, 33(3), pp.185~252 (2005)
  7. G. Capitanio, "Legendrian graphs generated by tangential family germs", Proc. Edinb. Math. Soc, 49(1), pp.29~37 (2006)[DOI]
  8. J. H. Cheng, "Minimal surfaces in pseudoher-mitian geometry", Ann. Sc. Norm. Super. Pisa Cl. Sci., 4(1), pp.129~177 (2005)
  9. H. -L. Chiu, "An application of the moving frame method to integral geometry in the Heisenberg group", SIGMA Symmetry Integrability Geom. Methods Appl., 13, pp.27~ (2017)
  10. A general and intuitive envelope theorem, "A. Clausen", Edinburgh School of Economics, ~, pp.ESE Discussion Papers; No. 274 (2016)
  11. H. Edelsbrunner, "The upper envelope of piecewise linear functions : Algorithms and applications", Discrete & Computational Geometry, 4(4), pp.311~336 (1989)
  12. L. P. Eisenhart, "A Treatise on the Dierential Geometry of Curves and Surfaces" (1960), Dover Publications, Inc
  13. H. Geiges, "Cambridge Studies in Advanced Mathematics, 109" (2008), Cambridge University Press
  14. M. C. Griebelery, "General envelope theorems for multidimensional type spaces", The 31nd Meeting of the Brazilian Econometric Society (2009)
  15. M. Gromov, "Sub-Riemannian geometry", pp.79~323 (1996)
  16. J. Hershberger, "Finding the upper envelope of n line segments in O(n log n) time", Inform. Process. Lett, 33(4), pp.169~174 (1989)[DOI]
  17. Completely integrable rst-order partial dierential equations, "S. Izumiya", 12~31, pp.Surikaisekiken kyusho Kokyuroku No. 807 (1992)
  18. A. Kock, "Envelopes|notion and deniteness", Beitrage Algebra Geom, 48(2), pp.345~350 (2007)
  19. Y. Li, "Envelopes of Legendre curves in the unit spherical bundle over the unit sphere", Q. J. Math, 69(2), pp.631~653 (2018)[DOI]
  20. V. Marenich, "Geodesics in Heisenberg groups", Geom. Dedicata, 66(2), pp.175~185 (1997)[DOI]
  21. P. Milgrom, "Envelope theorems for arbitrary choice sets", Econometrica, 70(2), pp.583~601 (2002)[DOI]
  22. R. Monti, "Geodetically convex sets in the Heisenberg group", J. Convex Anal, 12(1), pp.187~196 (2005)
  23. M. Ritore, "Area-stationary surfaces in the Heisenberg group H1", Adv. Math, 219(2), pp.633~671 (2008)[DOI]
  24. "Integral Geometry and Geometric Probability" (2004)[URL]
  25. M. Takahashi, "Real and complex singularities", pp.337~355 (2016)
  26. R. Thom, "Sur la theorie des enveloppes", J. Math. Pures Appl., 41(9), pp.177~192 (1962)
  27. V. M. Zakalyukin, "Envelopes of wave front families, and control theory", Trudy Mat. Inst. Steklov, 209, pp.133~142 (1995)

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