MỘT SỐ KẾT QUẢ VỀ ĐƯỜNG CONG TRONG MẶT PHẲNG VỚI MẬT ĐỘ TUYẾN TÍNH

Authors

  • Đoàn Thế Hiếu Trường Đại học Sư phạm
  • Nguyễn Minh Hoàng

Abstract

We study some problems concerning to the notion of curvature with densityof curves in planes with density such as The Four Vertex Theorem and someextremum problems of isoperimetric type in the plane with density ex

References

C. Borell, The Brunn-Minkowski inequality in Gauss space, Invent. Math. 30

(1975), 207-216.

M. P. do Carmo, Differential geometry of curves and surfaces, Prentice-Hall,

Englewood Cliffs, NJ, 1976.

I. Corwin, N. Hoffman, S. Hurder, V. Sesum, and Y. Xu, Differential geometry

of manifolds with density, Rose-Hulman Und. Math. J., 7 (1) (2006).

M. Gromov, Isoperimetry of waists and concentration of maps, Geom. Funct.

Anal., 13 (2003), 178-215.

D. T. Hieu, T. L. Nam On the four vertex theorem in planes with radial density

e'(r), Colloq. Math., Vol. 113, No 1 (2008), 169-174.

F. Morgan, Manifolds with density, Notices Amer. Math. Soc., 52 (2005), 853-

C. Rosales, A. Canete, V. Bayle, and F. Morgan, On the isoperimetric problem

in Euclidean space with density, Calc. Var. PDE 31 (2008),27-46.

D. DeTurck, H. Gluck, D. Pomerleano and D. S. Vick, The Four Vertex Theorem

and Its Converse, Notices AMS., Vol. 54, No 2 (2007), 192-207.

Published

2013-03-22