Pacific Journal of Mathematics

The structure of singularities in $\Phi$-minimizing networks in ${\bf R}^2$.

Manuel Alfaro, Mark Conger, Kenneth Hodges, and et al.

Article information

Pacific J. Math., Volume 149, Number 2 (1991), 201-210.

First available in Project Euclid: 8 December 2004

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 90C35: Programming involving graphs or networks [See also 90C27]
Secondary: 49Q99: None of the above, but in this section


Alfaro, Manuel; Conger, Mark; Hodges, Kenneth; al., et. The structure of singularities in $\Phi$-minimizing networks in ${\bf R}^2$. Pacific J. Math. 149 (1991), no. 2, 201--210.

Export citation


  • [Ab] J. Abrahamson, Curveslength minimizing modulo v in Rn , Michigan Math. J., 35 (1988), 285-290.
  • [Al] M. Alfaro et al., Segments can meet in fours in energy-minimizing networks, J. of Undergraduate Math., 22 (1990), 9-20.
  • [B] R. Bassini, Length-minimizing networksfor threepoints in R2, undergraduate research, M.I.T.,preprint, 1982.
  • [C] E. J. Cockayne, On the Steiner problem, Canad. Math. Bull., 10 (1967), 431- 450.
  • [Con] Mark Conger, Energy-minimizing networks in R" , Honors thesis, Williams College, 1989, expanded 1989.
  • [CR] R. Courant and H. Robbins, What is Mathematics*), Oxford University Press, 1941.
  • [F] H. Federer, GeometricMeasure Theory, Springer-Verlag, New York, 1969.
  • [H] M. Hanan, On Steiner's problem with rectilinear distance, J. SIAM Appl. Math., 14(1966), 255-265.
  • [L] A. Levy, Energy-minimizing networks meet only in threes,J. of Undergraduate Math., 22 (1990), 53-59.
  • [LM] Gary Lawlor and Frank Morgan, Minimizing cones and networks: immiscible fluids, norms, and calibrations,preprint (1991).
  • [Me] M. McCutchan,Size-minimizing curves,undergraduate research, M.I.T.,pre- print, 1986.
  • [Ml] F. Morgan, The cone over the Clifford torus in R4 is -minimizing, Math. Ann., to appear (1991).
  • [M2] F. Morgan, GeometricMeasure Theory: A Beginner's Guide,Academic Press, 1988.
  • [M3] F. Morgan, Riemannian Geometry: A Beginner's Guide, manuscript, 1991.
  • [T] J. Taylor, Crystalline variationalproblems, Bull. Amer. Math. Soc, 84 (1978), 568-588.