- NOTES AND COMMENTARY 255
§4. This section follows §11 and § 12 of Hamilton [143]. For background
and more advanced topics on minimal surfaces we refer the reader to Colding and
Minicozzi [86], Lawson [183], and Osserman [300].
The well-known Smith conjecture says that the fixed point set of a periodic
orientation-preserving diffeomorphism of S^3 is either empty or an unknotted circle
(seep. 4 of Morgan and Bass [250]).
A different proof of the most important case of Schoen and Yau's positive
energy theorem, using spinors, was given soon thereafter by Witten [437] (see also
Parker and Taubes [305]).
As we mentioned in the introduction to this chapter, see §8 of Perelman [313]
and §93.l of Kleiner and Lott [161] for other approaches to the proof of the incom-
pressibility of the cuspidal tori.
Proposition 33 .24 is Theorem 11.l in [143].
We have the following correspondences with results in § 12 of [143]. Lemma
33.34 is Theorem 12 .l in [143]. For Corollary 33.35, see Corollary 12.2 in [143].
For Corollary 33.36, see Corollary 12 .4 in [143]. For Lemma 33.37 see Lemma 12.5
in [143]. Lemma 33.39 is Corollary 12 .7 in [143].