### Double bubbles minimize.

Hass, Joel, Schlafly, Roger (2000)

Annals of Mathematics. Second Series

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Hass, Joel, Schlafly, Roger (2000)

Annals of Mathematics. Second Series

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Robert Connelly (1977)

Publications Mathématiques de l'IHÉS

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International Journal of Mathematics and Mathematical Sciences

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Cox, S.J., Flikkema, E. (2010)

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Hass, Joel, Hutchings, Michael, Schlafly, Roger (1995)

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Krushkal, Vyacheslav S., Quinn, Frank (2000)

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J. Carter, Masahico Saito (1998)

Banach Center Publications

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A necessary and sufficient condition for an immersed surface in 3-space to be lifted to an embedding in 4-space is given in terms of colorings of the preimage of the double point set. Giller's example and two new examples of non-liftable generic surfaces in 3-space are presented. One of these examples has branch points. The other is based on a construction similar to the construction of Giller's example in which the orientation double cover of a surface with odd Euler characteristic...

Harold Rosenberg (1991-1992)

Séminaire Bourbaki

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Hoffman, David, Wei, Fusheng (2002)

Experimental Mathematics

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