Potential Theory on Minimal Hypersurfaces I: Singularities as Martin Boundaries
Tóm tắt
Area minimizing hypersurfaces and, more generally, almost minimizing hypersurfaces frequently occur in geometry, dynamics and physics. A central problem is that a general (almost) minimizing hypersurface H contains a complicated singular set Σ. Regardless of this we can develop a detailed potential theory on H ∖Σ applicable to large classes of linear elliptic second order operators. We even get a fine control over their analysis near Σ. The present paper is the foundational Part 1 of this two parts work.
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