Is there a standard natural candidate surface for the shape that encloses three given volumes in $\mathbb{R}^3$ and has minimal surface area?
I know the planar triple bubble conjecture was proved by Wacharin Wichiramala in 2004 in a paper that I cannot access now ("Proof of the planar triple bubble conjecture." Journal fur die Reine und Angewandte Mathematik 567 (2004): 1-49). I am guessing this paper may describe the candidate in $\mathbb{R}^3$. Perhaps "the" is already incorrect, in that there may be several candidate surfaces? If so, the question could be narrowed to three equal volumes.
Ultimately I am seeking an image of the candidate(s), but any help here would be appreciated—Thanks!
Thanks for everyone's help! (I posted this summary at the same time j.c. was providing his comprehensive answer.) Here is an image made by John Sullivan: "a standard cluster of three bubbles, where the surfaces are spherical. Any three desired volumes can be achieved by a Möbius transformation of this cluster":
And here is a photograph found at this link:
(Added 9Mar14) j.c. found the original photo of the above and noticed it actually has a tiny 4th bubble!