A Level Set Analysis of the Witten Spinor with Applications to Curvature Estimates

Details A Level Set Analysis of the Witten Spinor with Applications to Curvature Estimates A Level Set Analysis of the Witten Spinor with Applications to Curvature Estimates

2007-01-29

arxiv.org/abs/math/0701864v3

Math. Res. Lett. 16 (2009) 41-55

Mathematics

Differential Geometry

15 pages, LaTeX (published version)

Scientific paper

We analyze the level sets of the norm of the Witten spinor in an asymptotically flat Riemannian spin manifold of positive scalar curvature. Level sets of small area are constructed. We prove curvature estimates which quantify that, if the total mass becomes small, the manifold becomes flat with the exception of a set of small surface area. These estimates involve either a volume bound or a spectral bound for the Dirac operator on a conformal compactification, but they are independent of the isoperimetric constant.

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