Inductive Analysis on Singular Minimal Hypersurfaces

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Lohkamp, Joachim
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The present paper describes a way to relate Martin boundaries on spaces of varying topology. This enables us to approach some detailed inductive analysis of the eigenfunctions of conformal Laplacians on minimal hypersurfaces near their singularities. This can directly be used resp. translated to understand the way how such minimal hypersurfaces inherit positive scalar curvature from their ambience resp. how to smooth singular minimal hypersurfaces to regular hypersurfaces with positive mean curvature.
Comment: This paper was submitted for publication as a part of a largely extended version of "Singular Minimal Hypersurfaces and Positive Scalar Curvature" math.DG/0609338 several months ago. We now put it on the web separately, since it will be instructive for the study of smoothing of singular minimal hypersurfaces via introduction of obstacles
Keywords
Mathematics - Differential Geometry, Mathematics - Analysis of PDEs, 53C21
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