The Least-Perimeter Partition of a Sphere into Four Equal Areas

Discrete and Computational Geometry

Volumn 44, Issue 3, 2010, Pages 645-653

  Engelstein, Max ^a  

^a YALE UNIVERSITY   (United States)

Author keywords

Isoperimetric problem; Minimal partitions; Tetrahedral partition

Indexed keywords

EID: 77955678932     PISSN: 01795376     EISSN: 14320444     Source Type: Journal    
DOI: 10.1007/s00454-009-9197-8     Document Type: Article

References (12)

1. Almgren, F. J. Jr., Taylor, J. E.: Geometry of soap films. Sci. Am. 235, 82-93 (1976).
2. Bernstein, F.: Über die isoperimetrische Eigenschaft des Kreises auf der Kugeloberfläche und in der Ebene. Math. Ann. 60, 117-136 (1905).
3. Engelstein, M., Maurmann, Q., Marcuccio, A., Pritchard, T.: Sphere partitions and density problems. NY J. Math. 15, 97-123 (2009).
4. Fejes Tóth, L.: Regular Figures. Pergamon Press, New York (1964).
5. Hales, T.: The honeycomb conjecture. Discrete Comput. Geom. 25, 1-22 (2001).
6. Hales, T.: The honeycomb conjecture on the sphere. Arxiv. org (2002).
7. Heppes, A.: On surface-minimizing polyhedral decompositions. Discrete Comput. Geom. 13, 529-539 (1995).
8. Lemarle, E.: Sur la stabilité des systèmes liquides en lames minces. Mém. Acad. R. Belg. 35, 3-104 (1864).
9. 2. Real Anal. Exch. 22, 1-10 (1996).
10. Maurmann, Q., Engelstein, M., Marcuccio, A., Pritchard, T.: Asymptotics of perimeter-minimizing partitions. Can. Math. Bull. (2009, to appear).
11. 2 and in surfaces. Pac. J. Math. 165, 347-361 (1994).
12. Quinn, C.: Least-perimeter partitions of the sphere. Rose-Hulman Und. Math. J. 8(2) (2007).