Araştırma Makalesi
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CURVATURE MOTION IN TIME-DEPENDENT MINKOWSKI PLANES

Yıl 2015, Cilt: 8 Sayı: 2, 70 - 81, 30.10.2015

Vitor Balestro

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

Öz


Anahtar Kelimeler

curvature motion minkowski plane isoperimetric inequality

Kaynakça

  • [1] Balestro, V., Craizer, M., Teixeira, R.: Curvature motion in a Minkowski Plane, unpublished work.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).

Yıl 2015, Cilt: 8 Sayı: 2, 70 - 81, 30.10.2015

Vitor Balestro

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

Öz

Kaynakça

  • [1] Balestro, V., Craizer, M., Teixeira, R.: Curvature motion in a Minkowski Plane, unpublished work.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).
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Vitor Balestro Bu kişi benim

Yayımlanma Tarihi 30 Ekim 2015
Yayımlandığı Sayı Yıl 2015 Cilt: 8 Sayı: 2

Kaynak Göster

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. Ekim 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, sy. 2 (Ekim 2015): 70-81. https://doi.org/10.36890/iejg.592288.
EndNote Balestro V (01 Ekim 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., c. 8, sy. 2, ss. 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 (Ekim 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, c. 8, sy. 2, 2015, ss. 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.