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Hypersurfaces in $ {\bf R}\sp n$ whose unit normal has small BMO norm


Author: Stephen Semmes
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
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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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1065093-4
Article copyright: © Copyright 1991 American Mathematical Society

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