[過去ﾛｸﾞ] ガロア第一論文と乗数イデアル他関連資料スレ11 (1002ﾚｽ)
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803(1): 12/28(土)11:49 ID:27qHSX8Z(1) AAS
This paper provides a new definition of the Ricci flow on closed manifolds admitting
harmonic spinors. It is shown that Perelman’s Ricci flow entropy can be expressed in
terms of the energy of harmonic spinors in all dimensions, and in four dimensions,
in terms of the energy of Seiberg–Witten monopoles. Consequently, Ricci flow is the
gradient flowoftheseenergies.Theproofreliesonaweightedversionofthemonopole
equations, introduced here. Further, a sharp parabolic Hitchin–Thorpe inequality for
simply-connected,spin4-manifoldsisproven.Fromthis,itfollowsthatthenormalized
Ricci flow on any exotic K3 surface must become singular.

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