• InS 3, when each enclosed volume and the complement occupy at least 10% of the volume ofS 3.
• inH 3, when the smaller volume is at least 85% that of the larger.
A balancing argument and asymptotic analysis reduce the problem inS 3 andH 3 to some computer checking. The computer analysis has been designed and fully implemented for both spaces.
Math Subject Classifications53C42
Key Words and PhrasesDouble bubbles
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- Álvarez, M. C., Corneli, J., Walsh, G., and Beheshti, S. Double bubbles in the three-torus,J. Experimental Math. 12, 79–89, (2000).Google Scholar
- Corneli, J. Double bubbles in spaces of constant curvature, undergraduate thesis, New College of Florida, 2002.Google Scholar
- Corneli, J., Corwin, I., Hurder, S., Sesum, V., Xu, Y., Adams, E., Davis, D., Lee, M., and Visocchi, R. Double bubbles in Gauss space and spheres,Houston J. Math., to appear.Google Scholar
- Corneli, J., Hoffman, N., Holt, P., Lee, G., Leger, N., Moseley, S., and Schoenfeld, E. Double Bubbles inS 3 andH 3, to appear at arXiv.org.Google Scholar
- Corneli, J., Hoffman, N. and Moseley, S. Double bubbles inS 3 andH 3 andG m, Williams College NSF SMALL undergraduate research Geometry Group report, 2003.Google Scholar
- Corneli, J., Holt, P., Leger, N., and Schoenfeld, E. Double bubbles inS 3 andH 3, Williams College NSF SMALL undergraduate research Geometry Group report, 2001.Google Scholar
- Heilman, C., Lai, Y., Reichardt, B., and Spielman, A. Component bounds for area-minimizing double bubbles, NSF “SMALL” undergraduate research Geometry Group report, Williams College, (Chapter 14), 1999.Google Scholar
- Hoffman, N. Double Bubbles inS 3,H 3 and Gauss Space, undergraduate thesis, Williams College, 2004.Google Scholar
- Wolfram, S.Mathematica Version 5, Wolfram Research, Champaign, 2003.Google Scholar