Research Article
BibTex RIS Cite

CURVATURE MOTION IN TIME-DEPENDENT MINKOWSKI PLANES

Year 2015, Volume: 8 Issue: 2, 70 - 81, 30.10.2015

Vitor Balestro

https://doi.org/10.36890/iejg.592288

Abstract


Keywords

curvature motion minkowski plane isoperimetric inequality

References

  • [1] Balestro, V., Craizer, M., Teixeira, R.: Curvature motion in a Minkowski Plane, unpublished work. Avaliable at: http://arxiv.org/abs/1407.5118 (2014).
  • [2] Craizer, M. : Iteration of involutes of constant width curves in the Minkowski plane, to appear in Beitr. Algebra Geom. (2014).
  • [3] Flanders, H.: A proof of Minkowski’s inequality for convex curves, Amer. Math. Monthly 75 (1969) 581-593.
  • [4] Gage, M.: Evolving plane curves by curvature in relative geometries, Duke Math J. 72 (1993) 441-466.
  • [5] Gage, M. & Li, Y., Evolving plane curves by curvature in relative geometries II, Duke Math J. 75 (1994) 79-98.
  • [6] Gage, M.: An isoperimetric inequality with applications to curve shortening, Duke Math. J. 50 (1983) 1225 - 1229.
  • [7] Gage, M.: Curve shortening makes convex curves circular, Invent. Math 76 (1984) 357 - 364.
  • [8] Gage, M. & Hamilton, R.S.: The heat equation shrinking convex plane curves, J. Diff. Geom.23 (1986) 69 - 96.
  • [9] Grayson, M.A. : The heat equation shrinks embedded planes curves to round points, J. Diff. Geom. 26 (1987) 285 - 314.
  • [10] Martini, H., Swanepoel, K.J., Weiss, G.: The geometry of Minkowski spaces- a survey. Part I, Expositiones Math. 19 (2001), 97 - 142.
  • [11] Martini, H., Swanepoel, K.J.: The geometry of Minkowski spaces- a survey. Part II, Expo- sitiones Math. 22 (2004), 93 - 144.
  • [12] Osserman, R.: Bonnesen-style isoperimetric inequalities, Amer. Math. Monthly 86 (1979).
  • [13] Petty, C.M. : On the geometry of the Minkowski plane, Riv. Math. Univ. Parma, 6 (1955), 269 - 292.
  • [14] Tabachnikov, S.: Parameterized plane curves, Minkowski caustics, Minkowski vertices and conservative line fields, L’Enseig. Math., 43 (1997), 3 - 26.
  • [15] Thompson, A.C.: Minkowski Geometry, Encyclopedia of Mathematics and its Applications, 63. Cambridge University Press, (1996).

Year 2015, Volume: 8 Issue: 2, 70 - 81, 30.10.2015

Vitor Balestro

https://doi.org/10.36890/iejg.592288

Abstract

References

  • [1] Balestro, V., Craizer, M., Teixeira, R.: Curvature motion in a Minkowski Plane, unpublished work. Avaliable at: http://arxiv.org/abs/1407.5118 (2014).
  • [2] Craizer, M. : Iteration of involutes of constant width curves in the Minkowski plane, to appear in Beitr. Algebra Geom. (2014).
  • [3] Flanders, H.: A proof of Minkowski’s inequality for convex curves, Amer. Math. Monthly 75 (1969) 581-593.
  • [4] Gage, M.: Evolving plane curves by curvature in relative geometries, Duke Math J. 72 (1993) 441-466.
  • [5] Gage, M. & Li, Y., Evolving plane curves by curvature in relative geometries II, Duke Math J. 75 (1994) 79-98.
  • [6] Gage, M.: An isoperimetric inequality with applications to curve shortening, Duke Math. J. 50 (1983) 1225 - 1229.
  • [7] Gage, M.: Curve shortening makes convex curves circular, Invent. Math 76 (1984) 357 - 364.
  • [8] Gage, M. & Hamilton, R.S.: The heat equation shrinking convex plane curves, J. Diff. Geom.23 (1986) 69 - 96.
  • [9] Grayson, M.A. : The heat equation shrinks embedded planes curves to round points, J. Diff. Geom. 26 (1987) 285 - 314.
  • [10] Martini, H., Swanepoel, K.J., Weiss, G.: The geometry of Minkowski spaces- a survey. Part I, Expositiones Math. 19 (2001), 97 - 142.
  • [11] Martini, H., Swanepoel, K.J.: The geometry of Minkowski spaces- a survey. Part II, Expo- sitiones Math. 22 (2004), 93 - 144.
  • [12] Osserman, R.: Bonnesen-style isoperimetric inequalities, Amer. Math. Monthly 86 (1979).
  • [13] Petty, C.M. : On the geometry of the Minkowski plane, Riv. Math. Univ. Parma, 6 (1955), 269 - 292.
  • [14] Tabachnikov, S.: Parameterized plane curves, Minkowski caustics, Minkowski vertices and conservative line fields, L’Enseig. Math., 43 (1997), 3 - 26.
  • [15] Thompson, A.C.: Minkowski Geometry, Encyclopedia of Mathematics and its Applications, 63. Cambridge University Press, (1996).
There are 15 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Vitor Balestro This is me

Publication Date October 30, 2015
Published in Issue Year 2015 Volume: 8 Issue: 2

Cite

APA Balestro, V. (2015). CURVATURE MOTION IN TIME-DEPENDENT MINKOWSKI PLANES. International Electronic Journal of Geometry, 8(2), 70-81. https://doi.org/10.36890/iejg.592288
AMA Balestro V. CURVATURE MOTION IN TIME-DEPENDENT MINKOWSKI PLANES. Int. Electron. J. Geom. October 2015;8(2):70-81. doi:10.36890/iejg.592288
Chicago Balestro, Vitor. “CURVATURE MOTION IN TIME-DEPENDENT MINKOWSKI PLANES”. International Electronic Journal of Geometry 8, no. 2 (October 2015): 70-81. https://doi.org/10.36890/iejg.592288.
EndNote Balestro V (October 1, 2015) CURVATURE MOTION IN TIME-DEPENDENT MINKOWSKI PLANES. International Electronic Journal of Geometry 8 2 70–81.
IEEE V. Balestro, “CURVATURE MOTION IN TIME-DEPENDENT MINKOWSKI PLANES”, Int. Electron. J. Geom., vol. 8, no. 2, pp. 70–81, 2015, doi: 10.36890/iejg.592288.
ISNAD Balestro, Vitor. “CURVATURE MOTION IN TIME-DEPENDENT MINKOWSKI PLANES”. International Electronic Journal of Geometry 8/2 (October 2015), 70-81. https://doi.org/10.36890/iejg.592288.
JAMA Balestro V. CURVATURE MOTION IN TIME-DEPENDENT MINKOWSKI PLANES. Int. Electron. J. Geom. 2015;8:70–81.
MLA Balestro, Vitor. “CURVATURE MOTION IN TIME-DEPENDENT MINKOWSKI PLANES”. International Electronic Journal of Geometry, vol. 8, no. 2, 2015, pp. 70-81, doi:10.36890/iejg.592288.
Vancouver Balestro V. CURVATURE MOTION IN TIME-DEPENDENT MINKOWSKI PLANES. Int. Electron. J. Geom. 2015;8(2):70-81.