Hypersurfaces in $\textbf {R}^ n$ whose unit normal has small BMO norm
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- by Stephen Semmes PDF
- Proc. Amer. Math. Soc. 112 (1991), 403-412 Request permission
Abstract:
Let $M$ be a hypersurface in ${{\mathbf {R}}^{d + 1}}$ whose Gauss map has small BMO norm. This condition is closely related to (but much weaker than) the requirement that the principal curvatures of $M$ have small ${L^d}\left ( M \right )$ norm. (The relationship between these two conditions is a nonlinear geometrical analogue of a classical Sobolev embedding.) This paper deals with the problem of understanding the geometrical constraints imposed on $M$ by the requirement that the Gauss map have small BMO norm.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 112 (1991), 403-412
- MSC: Primary 53A05; Secondary 42B99, 53C40
- DOI: https://doi.org/10.1090/S0002-9939-1991-1065093-4
- MathSciNet review: 1065093